Integration over the quantum diagonal subgroup and associated Fourier-like algebras

By analogy with the classical construction due to Forrest, Samei and Spronk we associate to every compact quantum group $\mathbb{G}$ a completely contractive Banach algebra $A_\Delta(\mathbb{G})$, which can be viewed as a deformed Fourier algebra of $\mathbb{G}$. To motivate the construction we first analyse in detail the quantum version of the integration over the diagonal subgroup, showing that although the quantum diagonal subgroups in fact never exist, as noted earlier by Kasprzak and So{\l}tan, the corresponding integration represented by a certain idempotent state on $C(\mathbb{G})$ makes sense as long as $\mathbb{G}$ is of Kac type. Finally we analyse as an explicit example the algebras $A_\Delta(O_N^+)$, $N\ge 2$, associated to Wang's free orthogonal groups, and show that they are not operator weakly amenable.Comment: Minor updates; Remark 5.7 has been added; 31 page

Quantum Symmetries and Strong Haagerup Inequalities

In this paper, we consider families of operators $\{x_r\}_{r \in \Lambda}$ in a tracial C$^\ast$-probability space $(\mathcal A, \phi)$, whose joint $\ast$-distribution is invariant under free complexification and the action of the hyperoctahedral quantum groups $\{H_n^+\}_{n \in \N}$. We prove a strong form of Haagerup's inequality for the non-self-adjoint operator algebra $\mathcal B$ generated by $\{x_r\}_{r \in \Lambda}$, which generalizes the strong Haagerup inequalities for $\ast$-free R-diagonal families obtained by Kemp-Speicher \cite{KeSp}. As an application of our result, we show that $\mathcal B$ always has the metric approximation property (MAP). We also apply our techniques to study the reduced C$^\ast$-algebra of the free unitary quantum group $U_n^+$. We show that the non-self-adjoint subalgebra $\mathcal B_n$ generated by the matrix elements of the fundamental corepresentation of $U_n^+$ has the MAP. Additionally, we prove a strong Haagerup inequality for $\mathcal B_n$, which improves on the estimates given by Vergnioux's property RD \cite{Ve}

Menelaus' theorem, Clifford configurations and inversive geometry of the Schwarzian KP hierarchy

It is shown that the integrable discrete Schwarzian KP (dSKP) equation which constitutes an algebraic superposition formula associated with, for instance, the Schwarzian KP hierarchy, the classical Darboux transformation and quasi-conformal mappings encapsulates nothing but a fundamental theorem of ancient Greek geometry. Thus, it is demonstrated that the connection with Menelaus' theorem and, more generally, Clifford configurations renders the dSKP equation a natural object of inversive geometry on the plane. The geometric and algebraic integrability of dSKP lattices and their reductions to lattices of Menelaus-Darboux, Schwarzian KdV, Schwarzian Boussinesq and Schramm type is discussed. The dSKP and discrete Schwarzian Boussinesq equations are shown to represent discretizations of families of quasi-conformal mappings.Comment: 26 pages, 9 figure

Suspected idiopathic sclerosing orbital inflammation presenting as immunoglobulin G4-related disease: a case report

<p>Abstract</p> <p>Introduction</p> <p>Idiopathic sclerosing orbital inflammation is a rare and ill-defined heterogeneous entity, and a distinct subset of orbital inflammation. Recently, attention has been focused on immunoglobulin G4-related disease complicated with fibrotic changes in some other organs with high serum immunoglobulin G4 levels. This report presents a case of suspected idiopathic sclerosing orbital inflammation complicated with high serum immunoglobulin G4 levels.</p> <p>Case presentation</p> <p>An 82-year-old Japanese woman had a 30-year history of chronic thyroiditis. She experienced right ptosis and eyelid swelling. These symptoms gradually developed over five years. The clinical and radiographic findings suggested that our patient had idiopathic sclerosing orbital inflammation. We were unable to obtain our patient's consent to perform a biopsy. While the serum immunoglobulin G level was within the normal limits, the serum immunoglobulin G4 level was significantly elevated. The serum immunoglobulin G4 levels decreased after the administration of oral prednisolone at a daily dose of 20 mg. In addition, the swelling and ptosis of the right upper eyelid disappeared gradually after four weeks. Our patient was then suspected to have idiopathic sclerosing orbital inflammation complicated with immunoglobulin G4-related disease and chronic thyroiditis.</p> <p>Conclusion</p> <p>An orbital pseudotumor of this type is indicative of idiopathic sclerosing orbital inflammation immunoglobulin G4-related disease. Immunoglobulin G4 may thus be considered a subclass of immunoglobulin G when the serum immunoglobulin G level is within normal limits.</p

Revalidation and electronic cataract surgery audit: a Scottish survey on current practice and opinion

PURPOSE: To determine current knowledge and opinion on revalidation, and methods of cataract surgery audit in Scotland and to outline the current and future possibilities for electronic cataract surgery audit. METHODS: In 2010 we conducted a prospective, cross-sectional, Scottish-wide survey on revalidation knowledge and opinion, and cataract audit practice among all senior NHS ophthalmologists. Results were anonymised and recorded manually for analysis. RESULTS: In all, 61% of the ophthalmologists surveyed took part. Only 33% felt ready to take part in revalidation, whereas 76% felt they did not have adequate information about the process. Also, 71% did not feel revalidation would improve patient care, but 85% agreed that cataract surgery audit is essential for ophthalmic practice. In addition, 91% audit their cataract outcomes; 52% do so continuously. Further, 63% audit their subspecialist surgical results. Only 25% audit their cataract surgery practice electronically, and only 12% collect clinical data using a hospital PAS system. Funding and system incompatibility were the main reasons cited for the lack of electronic audit setup. Currently, eight separate hospital IT patient administration systems are used across 14 health boards in Scotland. CONCLUSION: Revalidation is set to commence in 2012. The Royal College of Ophthalmologists will use cataract outcome audit as a tool to ensure surgical competency for the process. Retrospective manual auditing of cataract outcome is time consuming, and can be avoided with an electronic system. Scottish ophthalmologists view revalidation with scepticism and appear to have inadequate knowledge of the process. However, they strongly agree with the concept of cataract surgery audit. The existing and future electronic applications that may support surgical audit are commercial electronic records, web-based applications, centrally funded software applications, and robust NHS connections between community and hospital

Prostaglandin E2 Prevents Hyperosmolar-Induced Human Mast Cell Activation through Prostanoid Receptors EP2 and EP4

Background: Mast cells play a critical role in allergic and inflammatory diseases, including exercise-induced bronchoconstriction (EIB) in asthma. The mechanism underlying EIB is probably related to increased airway fluid osmolarity that activates mast cells to the release inflammatory mediators. These mediators then act on bronchial smooth muscle to cause bronchoconstriction. In parallel, protective substances such as prostaglandin E2 (PGE2) are probably also released and could explain the refractory period observed in patients with EIB. Objective: This study aimed to evaluate the protective effect of PGE2 on osmotically activated mast cells, as a model of exercise-induced bronchoconstriction. Methods: We used LAD2, HMC-1, CD34-positive, and human lung mast cell lines. Cells underwent a mannitol challenge, and the effects of PGE2 and prostanoid receptor (EP) antagonists for EP1-4 were assayed on the activated mast cells. Beta-hexosaminidase release, protein phosphorylation, and calcium mobilization were assessed. Results: Mannitol both induced mast cell degranulation and activated phosphatidyl inositide 3-kinase and mitogen-activated protein kinase (MAPK) pathways, thereby causing de novo eicosanoid and cytokine synthesis. The addition of PGE2 significantly reduced mannitol-induced degranulation through EP2 and EP4 receptors, as measured by beta-hexosaminidase release, and consequently calcium influx. Extracellular-signal-regulated kinase 1/2, c-Jun N-terminal kinase, and p38 phosphorylation were diminished when compared with mannitol activation alone. Conclusions:Our data show a protective role for the PGE2 receptors EP2 and EP4 following osmotic changes, through the reduction of human mast cell activity caused by calcium influx impairment and MAP kinase inhibition

Exploring the role of HR practitioners in pursuit of organizational effectiveness in higher education institutions

This paper focuses on how HR professionals view their role in contributing to organizational effectiveness in the HE sector. Drawing on interview data, we trace how rival definitions of organizational effectiveness relate to two emergent conceptions of rationality. Firstly we identify instrumental forms of rationality based on assessments of how well (or efficiently) organisations achieve pre-ordained objectives. Secondly, we identify stakeholder satisfaction models of organisational effectiveness, which concern the extent to which competing needs of stakeholders are satisfied and, thus, presuppose a more dialogic view of rationality. The context for our discussion is the UK Higher Education sector and, drawing on our research, we argue that universities can be seen as moving from a stakeholder satisfaction model to an instrumentally rational model of organisational effectiveness. Our findings suggest that HR professionals do support attempts to re-orientate their institutions towards a top-down form of organisation, which would privilege high level objectives and efficiency (thus following the prescriptions of the New Public Management movement). This implies a move away from a more traditional view of universities as discursive and participatory organisations, where effectiveness is regarded as meeting the varied needs of stakeholders, such as academics, students and the wider society, in a balanced way. However, whilst the HRM professionals largely favour such a shift, they acknowledge limitations to the extent that is practical or even entirely desirable

Characterization of cis- and trans-acting elements in the imprinted human SNURF-SNRPN locus

The imprinted SNRPN locus is a complex transcriptional unit that encodes the SNURF and SmN polypeptides as well as multiple non-coding RNAs. SNRPN is located within the Prader-Willi and Angelman syndrome (PWS/AS) region that contains multiple imprinted genes, which are coordinately regulated by a bipartite imprinting center (IC). The SNRPN 5′ region co-localizes with the PWS-IC and contains two DNase I hypersensitive sites, DHS1 at the SNRPN promoter, and DHS2 within intron 1, exclusively on the paternally inherited chromosome. We have examined DHS1 and DHS2 to identify cis- and trans-acting regulatory elements within the endogenous SNRPN 5′ region. Analysis of DHS1 by in vivo footprinting and chromatin immunoprecipitation identified allele-specific interaction with multiple regulatory proteins, including NRF-1, which regulates genes involved in mitochondrial and metabolic functions. DHS2 acted as an enhancer of the SNRPN promoter and contained a highly conserved region that showed allele-specific interaction with unphosphorylated RNA polymerase II, YY1, Sp1 and NRF-1, further suggesting a key role for NRF-1 in regulation of the SNRPN locus. We propose that one or more of the regulatory elements identified in this study may also contribute to PWS-IC function

Phenotypic Plasticity of Mouse Spermatogonial Stem Cells

BACKGROUND:Spermatogonial stem cells (SSCs) continuously undergo self-renewal division to support spermatogenesis. SSCs are thought to have a fixed phenotype, and development of a germ cell transplantation technique facilitated their characterization and prospective isolation in a deterministic manner; however, our in vitro SSC culture experiments indicated heterogeneity of cultured cells and suggested that they might not follow deterministic fate commitment in vitro. METHODOLOGY AND PRINCIPAL FINDINGS:In this study, we report phenotypic plasticity of SSCs. Although c-kit tyrosine kinase receptor (Kit) is not expressed in SSCs in vivo, it was upregulated when SSCs were cultured on laminin in vitro. Both Kit(-) and Kit(+) cells in culture showed comparable levels of SSC activity after germ cell transplantation. Unlike differentiating spermatogonia that depend on Kit for survival and proliferation, Kit expressed on SSCs did not play any role in SSC self-renewal. Moreover, Kit expression on SSCs changed dynamically once proliferation began after germ cell transplantation in vivo. CONCLUSIONS/SIGNIFICANCE:These results indicate that SSCs can change their phenotype according to their microenvironment and stochastically express Kit. Our results also suggest that activated and non-activated SSCs show distinct phenotypes

Kinetic CRAC uncovers a role for Nab3 in determining gene expression profiles during stress

RNA-binding proteins play a key role in shaping gene expression profiles during stress, however, little is known about the dynamic nature of these interactions and how this influences the kinetics of gene expression. To address this, we developed kinetic cross-linking and analysis of cDNAs (\u3c7CRAC), an ultraviolet cross-linking method that enabled us to quantitatively measure the dynamics of protein\u2013RNA interactions in vivo on a minute time-scale. Here, using \u3c7CRAC we measure the global RNA-binding dynamics of the yeast transcription termination factor Nab3 in response to glucose starvation. These measurements reveal rapid changes in protein\u2013RNA interactions within 1\u2009min following stress imposition. Changes in Nab3 binding are largely independent of alterations in transcription rate during the early stages of stress response, indicating orthogonal transcriptional control mechanisms. We also uncover a function for Nab3 in dampening expression of stress-responsive genes. \u3c7CRAC has the potential to greatly enhance our understanding of in vivo dynamics of protein\u2013RNA interactions