The Bloch-Okounkov correlation functions, a classical half-integral case

Bloch and Okounkov's correlation function on the infinite wedge space has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, and certain character functions of \hgl_\infty-modules of level one. Recent works have calculated these character functions for higher levels for \hgl_\infty and its Lie subalgebras of classical type. Here we obtain these functions for the subalgebra of type $D$ of half-integral levels and as a byproduct, obtain $q$-dimension formulas for integral modules of type $D$ at half-integral level.Comment: v2: minor changes to the introduction; accepted for publication in Letters in Mathematical Physic

Evaluating Fire Temperatures During a Prescribed Burn of a Restored Tallgrass Prairie

Wildfire is recognized to have shaped the great prairies of the central US. While the vast majority of these grasslands have been lost there remain significant remnants as well as sites under active restoration. Prescribed fire is often used in these systems in order to maximize the success of the native grasses. Beginning in 1999 Cedarville University established a prairie restoration site and have used disturbances, such as fire, to maintain the system. Without this regular burn, the prairie would likely show decreased grass growth and increased growth of forb species. The Cedarville Prairie Restoration site has a variable topography, with several small hills and valleys. Such variations can affect the way that fire travels and burns. Therefore, our objective is to evaluate the relationships between prairie topography and fire temperature. We will use a 25 x 25 meter grid within the prairie, placing stakes attached to tags painted with thermo-sensitive paint at regular intervals along the grid. Following the prescribed fire in early April we will we analyze the tags to determine the temperature of the fire at each location on the grid. From this we will generate a heat intensity map in order to investigate patterns. In particular, we anticipate that the fire will burn at higher temperatures on slopes upward from its point of origin. We also anticipate that the fire will burn at lower temperatures in valley areas, due to moisture accumulation

The Bloch-Okounkov correlation functions of classical type

Bloch and Okounkov introduced an n-point correlation function on the infinite wedge space and found an elegant closed formula in terms of theta functions. This function has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, etc, and it can also be interpreted as correlation functions on integrable gl_\infty-modules of level one. Such gl_\infty-correlation functions at higher levels were then calculated by Cheng and Wang. In this paper, generalizing the type A results, we formulate and determine the n-point correlation functions in the sense of Bloch-Okounkov on integrable modules over classical Lie subalgebras of gl_\infty of type B,C,D at arbitrary levels. As byproducts, we obtain new q-dimension formulas for integrable modules of type B,C,D and some fermionic type q-identities.Comment: v2, very minor changes, Latex, 41 pages, to appear in Commun. Math. Phy

Displaced but not replaced: the impact of e-learning on academic identities in higher education.

Challenges facing universities are leading many to implement institutional strategies to incorporate e-learning rather than leaving its adoption up to enthusiastic individuals. Although there is growing understanding about the impact of e-learning on the student experience, there is less understanding of academics’ perceptions of e-learning and its impact on their identities. This paper explores the changing nature of academic identities revealed through case study research into the implementation of e-learning at one UK university. By providing insight into the lived experiences of academics in a university in which technology is not only transforming access to knowledge but also influencing the balance of power between academic and student in knowledge production and use, it is suggested that academics may experience a jolt to their ‘trajectory of self’ when engaging with e-learning. The potential for e-learning to prompt loss of teacher presence and displacement as knowledge expert may appear to undermine the ontological security of their academic identity

NC Calabi-Yau Orbifolds in Toric Varieties with Discrete Torsion

Using the algebraic geometric approach of Berenstein et {\it al} (hep-th/005087 and hep-th/009209) and methods of toric geometry, we study non commutative (NC) orbifolds of Calabi-Yau hypersurfaces in toric varieties with discrete torsion. We first develop a new way of getting complex $d$ mirror Calabi-Yau hypersurfaces $H_{\Delta}^{\ast d}$ in toric manifolds $M_{\Delta }^{\ast (d+1)}$ with a $C^{\ast r}$ action and analyze the general group of the discrete isometries of $H_{\Delta}^{\ast d}$. Then we build a general class of $d$ complex dimension NC mirror Calabi-Yau orbifolds where the non commutativity parameters $\theta_{\mu \nu}$ are solved in terms of discrete torsion and toric geometry data of $M_{\Delta}^{(d+1)}$ in which the original Calabi-Yau hypersurfaces is embedded. Next we work out a generalization of the NC algebra for generic $d$ dimensions NC Calabi-Yau manifolds and give various representations depending on different choices of the Calabi-Yau toric geometry data. We also study fractional D-branes at orbifold points. We refine and extend the result for NC $T^{2})/(\mathbf{{Z_{2}}\times {Z_{2})}}$ to higher dimensional torii orbifolds in terms of Clifford algebra.Comment: 38 pages, Late

Chemical-potential standard for atomic Bose-Einstein condensates

When subject to an external time periodic perturbation of frequency $f$, a Josephson-coupled two-state Bose-Einstein condensate responds with a constant chemical potential difference $\Delta\mu=khf$, where $h$ is Planck's constant and $k$ is an integer. We propose an experimental procedure to produce ac-driven atomic Josephson devices that may be used to define a standard of chemical potential. We investigate how to circumvent some of the specific problems derived from the present lack of advanced atom circuit technology. We include the effect of dissipation due to quasiparticles, which is essential to help the system relax towards the exact Shapiro resonance, and set limits to the range of values which the various physical quantities must have in order to achieve a stable and accurate chemical potential difference between the macroscopic condensates.Comment: 13 pages, 4 figure

The broad phenotypic spectrum of 17α-hydroxylase/17,20-lyase (CYP17A1) deficiency: a case series

CONTEXT: 17α-Hydroxylase/17,20-lyase deficiency (17OHD) caused by mutations in the CYP17A1 gene is a rare form of congenital adrenal hyperplasia typically characterised by cortisol deficiency, mineralocorticoid excess and sex steroid deficiency. OBJECTIVE: To examine the phenotypic spectrum of 17OHD by clinical and biochemical assessment and corresponding in silico and in vitro functional analysis. DESIGN: Case series. PATIENTS AND RESULTS: We assessed eight patients with 17OHD, including four with extreme 17OHD phenotypes: two siblings presented with failure to thrive in early infancy and two with isolated sex steroid deficiency and normal cortisol reserve. Diagnosis was established by mass spectrometry-based urinary steroid profiling and confirmed by genetic CYP17A1 analysis, revealing homozygous and compound heterozygous sequence variants. We found novel (p.Gly111Val, p.Ala398Glu, p.Ile371Thr) and previously described sequence variants (p.Pro409Leu, p.Arg347His, p.Gly436Arg, p.Phe53/54del, p.Tyr60IlefsLys88X). In vitro functional studies employing an overexpression system in HEK293 cells showed that 17,20-lyase activity was invariably decreased while mutant 17α-hydroxylase activity retained up to 14% of WT activity in the two patients with intact cortisol reserve. A ratio of urinary corticosterone over cortisol metabolites reflective of 17α-hydroxylase activity correlated well with clinical phenotype severity. CONCLUSION: Our findings illustrate the broad phenotypic spectrum of 17OHD. Isolated sex steroid deficiency with normal stimulated cortisol has not been reported before. Attenuation of 17α-hydroxylase activity is readily detected by urinary steroid profiling and predicts phenotype severity. SIGNIFICANCE STATEMENT: Here we report, supported by careful phenotyping, genotyping and functional analysis, a prismatic case series of patients with congenital adrenal hyperplasia due to 17α-hydroxylase (CYP17A1) deficiency (17OHD). These range in severity from the abolition of function, presenting in early infancy, and unusually mild with isolated sex steroid deficiency but normal ACTH-stimulated cortisol in adult patients. These findings will guide improved diagnostic detection of CYP17A1 deficiency

Climate change alterations to ecosystem dominance: how might sponge-dominated reefs function?

Anthropogenic stressors are impacting ecological systems across the world. Of particular concern are the recent rapid changes occurring in coral reef systems. With ongoing degradation from both local and global stressors, future reefs are likely to function differently to current coral-dominated ecosystems. Determining key attributes of future reef states is critical to reliably predict outcomes for ecosystem service provision. Here we explore the impacts of changing sponge dominance on coral reefs. Qualitative modelling of reef futures suggests that changing sponge dominance due to increased sponge abundance will have different outcomes for other trophic levels compared with increased sponge dominance as a result of declining coral abundance. By exploring uncertainty in the model outcomes we identify the need to: i) quantify changes in carbon flow through sponges, ii) determine the importance of food limitation for sponges, iii) assess the ubiquity of the recently described 'sponge loop', iv) determine the competitive relationships between sponges and other benthic taxa, particularly algae, and v) understand how changing dominance of other organisms alters trophic pathways and energy flows through ecosystems. Addressing these knowledge gaps will facilitate development of more complex models that assess functional attributes of sponge-dominated reef ecosystems. This article is protected by copyright. All rights reserved

Comparing Common Techniques for Calculating Parasite Prevalence

Raccoons (Procyon lotor) are the final host for raccoon roundworms (Baylisascaris procyonis). Raccoon roundworm is the leading cause of a dangerous neurological disease, known as larva migrans encephalopathy. Diagnostic tools for detecting the presence of B. procyonis within a raccoon population include necropsy, fecal flotation, and latrine analysis. Necropsies yield the highest measure of prevalence, with fecal flotation and latrine analysis often underestimating infection rates. We necropsied 225 raccoons gathered from 10 townships of Clark and Greene Counties in Ohio. We collected fecal samples from 95 raccoons negative for B. procyonis at necropsy. We suspended the feces in Sheather’s solution to float any eggs, and prepared slides from this solution. Nearly 14% of raccoons negative at necropsy for B. procyonis possessed eggs in their feces. We used a chi squared test for equality of distributions to determine the likelihood that a positive fecal analysis is related to B. procyonis prevalence or to the area in which the raccoon was trapped. These data will help us determine how well fecal analyses estimate parasite prevalence