Hilbert Series for Moduli Spaces of Two Instantons

The Hilbert Series (HS) of the moduli space of two G instantons on C^2, where G is a simple gauge group, is studied in detail. For a given G, the moduli space is a singular hyperKahler cone with a symmetry group U(2) \times G, where U(2) is the natural symmetry group of C^2. Holomorphic functions on the moduli space transform in irreducible representations of the symmetry group and hence the Hilbert series admits a character expansion. For cases that G is a classical group (of type A, B, C, or D), there is an ADHM construction which allows us to compute the HS explicitly using a contour integral. For cases that G is of E-type, recent index results allow for an explicit computation of the HS. The character expansion can be expressed as an infinite sum which lives on a Cartesian lattice that is generated by a small number of representations. This structure persists for all G and allows for an explicit expressions of the HS to all simple groups. For cases that G is of type G_2 or F_4, discrete symmetries are enough to evaluate the HS exactly, even though neither ADHM construction nor index is known for these cases.Comment: 53 pages, 9 tables, 24 figure

The Cohen-Macaulay property of separating invariants of finite groups

In the case of finite groups, a separating algebra is a subalgebra of the ring of invariants which separates the orbits. Although separating algebras are often better behaved than the ring of invariants, we show that many of the criteria which imply that the ring of invariants is non Cohen-Macaulay actually imply that no graded separating algebra is Cohen-Macaulay. For example, we show that, over a field of positive characteristic p, given sufficiently many copies of a faithful modular representation, no graded separating algebra is Cohen-Macaulay. Furthermore, we show that, for a p-group, the existence of a Cohen-Macaulay graded separating algebra implies the group is generated by bireflections. Furthermore, we show that, for a $p$-group, the existence of a Cohen-Macaulay graded separating algebra implies the group is generated by bireflections. Additionally, we give an example which shows that Cohen-Macaulay separating algebras can occur when the ring of invariants is not Cohen-Macaulay.Comment: We removed the conjecture which appeared in previous versions: we give a counter-example. We fixed the proof of Lemma 2.2 (previously Remark 2.2). 16 page

Methods in Mammary Gland Development and Cancer: the second ENDBC meeting - intravital imaging, genomics, modeling and metastasis

The second meeting of the European Network for Breast Development and Cancer (ENBDC) on 'Methods in Mammary Gland Development and Cancer' was held in April 2010 in Weggis, Switzerland. The focus was on genomics and bioinformatics, extracellular matrix and stroma-epithelial cell interactions, intravital imaging, the search for metastasis founder cells and mouse models of breast cancer

Nuclear Kaiso Expression Is Associated with High Grade and Triple-Negative Invasive Breast Cancer

Kaiso is a BTB/POZ transcription factor that is ubiquitously expressed in multiple cell types and functions as a transcriptional repressor and activator. Little is known about Kaiso expression and localization in breast cancer. Here, we have related pathological features and molecular subtypes to Kaiso expression in 477 cases of human invasive breast cancer. Nuclear Kaiso was predominantly found in invasive ductal carcinoma (IDC) (p = 0.007), while cytoplasmic Kaiso expression was linked to invasive lobular carcinoma (ILC) (p = 0.006). Although cytoplasmic Kaiso did not correlate to clinicopathological features, we found a significant correlation between nuclear Kaiso, high histological grade (p = 0.023), ERα negativity (p = 0.001), and the HER2-driven and basal/triple-negative breast cancers (p = 0.018). Interestingly, nuclear Kaiso was also abundant in BRCA1-associated breast cancer (p<0.001) and invasive breast cancer overexpressing EGFR (p = 0.019). We observed a correlation between nuclear Kaiso and membrane-localized E-cadherin and p120-catenin (p120) (p<0.01). In contrast, cytoplasmic p120 strongly correlated with loss of E-cadherin and low nuclear Kaiso (p = 0.005). We could confirm these findings in human ILC cells and cell lines derived from conditional mouse models of ILC. Moreover, we present functional data that substantiate a mechanism whereby E-cadherin controls p120-mediated relief of Kaiso-dependent gene repression. In conclusion, our data indicate that nuclear Kaiso is common in clinically aggressive ductal breast cancer, while cytoplasmic Kaiso and a p120-mediated relief of Kaiso-dependent transcriptional repression characterize ILC

Glycogen Synthase Kinase-3 regulates multiple myeloma cell growth and bortezomib-induced cell death

BACKGROUND: Glycogen Synthase Kinase-3 (GSK-3) \u3b1 and \u3b2 are two serine-threonine kinases controlling insulin, Wnt/\u3b2-catenin, NF-\u3baB signaling and other cancer-associated transduction pathways. Recent evidence suggests that GSK-3 could function as growth-promoting kinases, especially in malignant cells. In this study, we have investigated GSK-3\u3b1 and GSK-3\u3b2 function in multiple myeloma (MM). METHODS: GSK-3 \u3b1 and \u3b2 expression and cellular localization were investigated by Western blot (WB) and immunofluorescence analysis in a panel of MM cell lines and in freshly isolated plasma cells from patients. MM cell growth, viability and sensitivity to bortezomib was assessed upon treatment with GSK-3 specific inhibitors or transfection with siRNAs against GSK-3 \u3b1 and \u3b2 isoforms. Survival signaling pathways were studied with WB analysis. RESULTS: GSK-3\u3b1 and GSK-3\u3b2 were differently expressed and phosphorylated in MM cells. Inhibition of GSK-3 with the ATP-competitive, small chemical compounds SB216763 and SB415286 caused MM cell growth arrest and apoptosis through the activation of the intrinsic pathway. Importantly, the two inhibitors augmented the bortezomib-induced MM cell cytotoxicity. RNA interference experiments showed that the two GSK-3 isoforms have distinct roles: GSK-3\u3b2 knock down decreased MM cell viability, while GSK-3\u3b1 knock down was associated with a higher rate of bortezomib-induced cytotoxicity. GSK-3 inhibition caused accumulation of \u3b2-catenin and nuclear phospho-ERK1, 2. Moreover, GSK-3 inhibition and GSK-3\u3b1 knockdown enhanced bortezomib-induced AKT and MCL-1 protein degradation. Interestingly, bortezomib caused a reduction of GSK-3 serine phosphorylation and its nuclear accumulation with a mechanism that resulted partly dependent on GSK-3 itself. CONCLUSIONS: These data suggest that in MM cells GSK-3\u3b1 and \u3b2 i) play distinct roles in cell survival and ii) modulate the sensitivity to proteasome inhibitors

Which factors explain variation in intention to disclose a diagnosis of dementia? A theory-based survey of mental health professionals

Background: For people with dementia, patient-centred care should involve timely explanation of the diagnosis and its implications. However, this is not routine. Theoretical models of behaviour change offer a generalisable framework for understanding professional practice and identifying modifiable factors to target with an intervention. Theoretical models and empirical work indicate that behavioural intention represents a modifiable predictor of actual professional behaviour. We identified factors that predict the intentions of members of older people's mental health teams (MHTs) to perform key behaviours involved in the disclosure of dementia. Design: Postal questionnaire survey. Participants: Professionals from MHTs in the English National Health Service. Methods: We selected three behaviours: Determining what patients already know or suspect about their diagnosis; using explicit terminology when talking to patients; and exploring what the diagnosis means to patients. The questionnaire was based upon the Theory of Planned Behaviour (TPB), Social Cognitive Theory (SCT), and exploratory team variables. Main outcomes: Behavioural intentions. Results: Out of 1,269 professionals working in 85 MHTs, 399 (31.4%) returned completed questionnaires. Overall, the TPB best explained behavioural intention. For determining what patients already know, the TPB variables of subjective norm, perceived behavioural control and attitude explained 29.4% of the variance in intention. For the use of explicit terminology, the same variables explained 53.7% of intention. For exploring what the diagnosis means to patients, subjective norm and perceived behavioural control explained 48.6% of intention. Conclusion: These psychological models can explain up to half of the variation in intention to perform key disclosure behaviours. This provides an empirically- supported, theoretical basis for the design of interventions to improve disclosure practice by targeting relevant predictive factors. Trial Registration: ISRCTN15871014

Extracellular Sulfatases, Elements of the Wnt Signaling Pathway, Positively Regulate Growth and Tumorigenicity of Human Pancreatic Cancer Cells

BACKGROUND: Heparan sulfate proteoglycans (HSPGs) are control elements in Wnt signaling, which bind extracellularly to Wnt ligands and regulate their ability to interact with signal transduction receptors on the cell surface. Sulf-1 and Sulf-2 are novel extracellular sulfatases that act on internal glucosamine-6-sulfate (6S) modifications within HSPGs and thereby modulate HSPG interactions with various signaling molecules, including Wnt ligands. Emerging evidence indicates the importance of reactivated Wnt signaling in a number of cancers, including pancreatic adenocarcinoma. PRINCIPLE FINDINGS: Both Sulf proteins were upregulated in human pancreatic adenocarcinoma tumors and were broadly expressed in human pancreatic adenocarcinoma cell lines. Expression of human extracellular sulfatases Sulf-1 and Sulf-2 enhanced Wnt signaling in a reconstituted system. Three of four pancreatic adenocarcinoma cell lines tested exhibited autocrine Wnt signaling, in that extracellular Wnt ligands were required to initiate downstream Wnt signaling. Exposure of these pancreatic adenocarcinoma cells to a catalytically inactive form of Sulf-2 or siRNA-mediated silencing of endogenous Sulf-2 inhibited both Wnt signaling and cell growth. Sulf-2 silencing in two of these lines resulted in markedly reduced tumorigenesis in immunocompromised mice. CONCLUSIONS/SIGNIFICANCE: We have identified the Sulfs as potentiators of autocrine Wnt signaling in pancreatic cancer cells and have demonstrated their contribution to the growth and tumorigenicity of these cells. Since the Sulfs are extracellular enzymes, they would be attractive targets for therapy of pancreatic cancer. Our results run counter to the prevailing view in the literature that the Sulfs are negative regulators of tumorigenesis

The intellectual structure and substance of the knowledge utilization field: A longitudinal author co-citation analysis, 1945 to 2004

<p>Abstract</p> <p>Background</p> <p>It has been argued that science and society are in the midst of a far-reaching renegotiation of the social contract between science and society, with society becoming a far more active partner in the creation of knowledge. On the one hand, new forms of knowledge production are emerging, and on the other, both science and society are experiencing a rapid acceleration in new forms of knowledge utilization. Concomitantly since the Second World War, the science underpinning the knowledge utilization field has had exponential growth. Few in-depth examinations of this field exist, and no comprehensive analyses have used bibliometric methods.</p> <p>Methods</p> <p>Using bibliometric analysis, specifically first author co-citation analysis, our group undertook a domain analysis of the knowledge utilization field, tracing its historical development between 1945 and 2004. Our purposes were to map the historical development of knowledge utilization as a field, and to identify the changing intellectual structure of its scientific domains. We analyzed more than 5,000 articles using citation data drawn from the Web of Science^®. Search terms were combinations of knowledge, research, evidence, guidelines, ideas, science, innovation, technology, information theory and use, utilization, and uptake.</p> <p>Results</p> <p>We provide an overview of the intellectual structure and how it changed over six decades. The field does not become large enough to represent with a co-citation map until the mid-1960s. Our findings demonstrate vigorous growth from the mid-1960s through 2004, as well as the emergence of specialized domains reflecting distinct collectives of intellectual activity and thought. Until the mid-1980s, the major domains were focused on innovation diffusion, technology transfer, and knowledge utilization. Beginning slowly in the mid-1980s and then growing rapidly, a fourth scientific domain, evidence-based medicine, emerged. The field is dominated in all decades by one individual, Everett Rogers, and by one paradigm, innovation diffusion.</p> <p>Conclusion</p> <p>We conclude that the received view that social science disciplines are in a state where no accepted set of principles or theories guide research (<it>i.e.</it>, that they are pre-paradigmatic) could not be supported for this field. Second, we document the emergence of a new domain within the knowledge utilization field, evidence-based medicine. Third, we conclude that Everett Rogers was the dominant figure in the field and, until the emergence of evidence-based medicine, his representation of the general diffusion model was the dominant paradigm in the field.</p

Highly symmetric POVMs and their informational power

We discuss the dependence of the Shannon entropy of normalized finite rank-1 POVMs on the choice of the input state, looking for the states that minimize this quantity. To distinguish the class of measurements where the problem can be solved analytically, we introduce the notion of highly symmetric POVMs and classify them in dimension two (for qubits). In this case we prove that the entropy is minimal, and hence the relative entropy (informational power) is maximal, if and only if the input state is orthogonal to one of the states constituting a POVM. The method used in the proof, employing the Michel theory of critical points for group action, the Hermite interpolation and the structure of invariant polynomials for unitary-antiunitary groups, can also be applied in higher dimensions and for other entropy-like functions. The links between entropy minimization and entropic uncertainty relations, the Wehrl entropy and the quantum dynamical entropy are described.Comment: 40 pages, 3 figure