Overview of (pro-)Lie group structures on Hopf algebra character groups

Character groups of Hopf algebras appear in a variety of mathematical and physical contexts. To name just a few, they arise in non-commutative geometry, renormalisation of quantum field theory, and numerical analysis. In the present article we review recent results on the structure of character groups of Hopf algebras as infinite-dimensional (pro-)Lie groups. It turns out that under mild assumptions on the Hopf algebra or the target algebra the character groups possess strong structural properties. Moreover, these properties are of interest in applications of these groups outside of Lie theory. We emphasise this point in the context of two main examples: The Butcher group from numerical analysis and character groups which arise from the Connes--Kreimer theory of renormalisation of quantum field theories.Comment: 31 pages, precursor and companion to arXiv:1704.01099, Workshop on "New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series", May 25-28, 2015, ICMAT, Madrid, Spai

Continuity properties of measurable group cohomology

A version of group cohomology for locally compact groups and Polish modules has previously been developed using a bar resolution restricted to measurable cochains. That theory was shown to enjoy analogs of most of the standard algebraic properties of group cohomology, but various analytic features of those cohomology groups were only partially understood. This paper re-examines some of those issues. At its heart is a simple dimension-shifting argument which enables one to `regularize' measurable cocycles, leading to some simplifications in the description of the cohomology groups. A range of consequences are then derived from this argument. First, we prove that for target modules that are Fr\'echet spaces, the cohomology groups agree with those defined using continuous cocycles, and hence they vanish in positive degrees when the acting group is compact. Using this, we then show that for Fr\'echet, discrete or toral modules the cohomology groups are continuous under forming inverse limits of compact base groups, and also under forming direct limits of discrete target modules. Lastly, these results together enable us to establish various circumstances under which the measurable-cochains cohomology groups coincide with others defined using sheaves on a semi-simplicial space associated to the underlying group, or sheaves on a classifying space for that group. We also prove in some cases that the natural quotient topologies on the measurable-cochains cohomology groups are Hausdorff.Comment: 52 pages. [Nov 22, 2011:] Major re-write with Calvin C. Moore as new co-author. Results from previous version strengthened and several new results added. [Nov 25, 2012:] Final version now available at springerlink.co

Aberrant lipid metabolism disrupts calcium homeostasis causing liver endoplasmic reticulum stress in obesity.

The endoplasmic reticulum (ER) is the main site of protein and lipid synthesis, membrane biogenesis, xenobiotic detoxification and cellular calcium storage, and perturbation of ER homeostasis leads to stress and the activation of the unfolded protein response. Chronic activation of ER stress has been shown to have an important role in the development of insulin resistance and diabetes in obesity. However, the mechanisms that lead to chronic ER stress in a metabolic context in general, and in obesity in particular, are not understood. Here we comparatively examined the proteomic and lipidomic landscape of hepatic ER purified from lean and obese mice to explore the mechanisms of chronic ER stress in obesity. We found suppression of protein but stimulation of lipid synthesis in the obese ER without significant alterations in chaperone content. Alterations in ER fatty acid and lipid composition result in the inhibition of sarco/endoplasmic reticulum calcium ATPase (SERCA) activity and ER stress. Correcting the obesity-induced alteration of ER phospholipid composition or hepatic Serca overexpression in vivo both reduced chronic ER stress and improved glucose homeostasis. Hence, we established that abnormal lipid and calcium metabolism are important contributors to hepatic ER stress in obesity

Potential climatic transitions with profound impact on Europe

We discuss potential transitions of six climatic subsystems with large-scale impact on Europe, sometimes denoted as tipping elements. These are the ice sheets on Greenland and West Antarctica, the Atlantic thermohaline circulation, Arctic sea ice, Alpine glaciers and northern hemisphere stratospheric ozone. Each system is represented by co-authors actively publishing in the corresponding field. For each subsystem we summarize the mechanism of a potential transition in a warmer climate along with its impact on Europe and assess the likelihood for such a transition based on published scientific literature. As a summary, the ‘tipping’ potential for each system is provided as a function of global mean temperature increase which required some subjective interpretation of scientific facts by the authors and should be considered as a snapshot of our current understanding. <br/

Hyaluronan Binding Motifs of USP17 and SDS3 Exhibit Anti-Tumor Activity

BACKGROUND: We previously reported that the USP17 deubiquitinating enzyme having hyaluronan binding motifs (HABMs) interacts with human SDS3 (suppressor of defective silencing 3) and specifically deubiquitinates Lys-63 branched polyubiquitination of SDS3 resulting in negative regulation of histone deacetylase (HDAC) activity in cancer cells. Furthermore, USP17 and SDS3 mutually interact with each other to block cell proliferation in HeLa cells but the mechanism for this inhibition in cell proliferation is not known. We wished to investigate whether the HABMs of USP17 were responsible for tumor suppression activity. METHODOLOGY/PRINCIPAL FINDINGS: Similarly to USP17, we have identified that SDS3 also has three consecutive HABMs and shows direct binding with hyaluronan (HA) using cetylpyridinium chloride (CPC) assay. Additionally, HA oligosaccharides (6-18 sugar units) competitively block binding of endogenous HA polymer to HA binding proteins. Thus, administration of HA oligosaccharides antagonizes the interaction between HA and USP17 or SDS3. Interestingly, HABMs deleted USP17 showed lesser interaction with SDS3 but retain its deubiquitinating activity towards SDS3. The deletion of HABMs of USP17 could not alter its functional regulation on SDS3-associated HDAC activity. Furthermore, to explore whether HABMs in USP17 and SDS3 are responsible for the inhibition of cell proliferation, we investigated the effect of USP17 and SDS3-lacking HABMs on cell proliferation by soft agar, apoptosis, cell migration and cell proliferation assays. CONCLUSIONS: Our results have demonstrated that these HABMs in USP17 and its substrate SDS3 are mainly involved in the inhibition of anchorage-independent tumor growth

Mesenchymal Stem Cells Secrete Multiple Cytokines That Promote Angiogenesis and Have Contrasting Effects on Chemotaxis and Apoptosis

We have previously shown that mesenchymal stem cells (MSC) improve function upon integration in ischemic myocardium. We examined whether specific cytokines and growth factors produced by MSCs are able to affect angiogenesis, cellular migration and apoptosis. Conditioned media (CM) was prepared by culturing MSC for 48 hours. CM displayed significantly elevated levels of VEGF, Monocyte Chemoattractant Protein-1 (MCP-1), macrophage inflammatory protein-1α (MIP-1α), MIP-1β and monokine induced by IFN-γ (MIG) compared to control media. MSC contained RNA for these factors as detected by RT-PCR. CM was able to induce angiogenesis in canine vascular endothelial cells. MCP-1 and MIP-1α increased cell migration of MSC while VEGF reduced it. H9c2 cells treated with CM under hypoxic conditions for 24 hours displayed a 16% reduction in caspase-3 activity compared to controls. PI 3-kinase γ inhibitor had no effect on controls but reversed the effect of CM on caspase-3 activity. MCP-1 alone mimicked the protective effect of CM while the PI 3-Kγ inhibitor did not reverse the effect of MCP-1. CM reduced phospho-BAD (Ser112) and phospho-Akt (Ser473) while increasing phospho-Akt (Thr308). MCP-1 reduced the level of phospho-Akt (Ser473) while having no effect on the other two; the PI 3-Kγ inhibitor did not alter the MCP-1 effect. ERK 1/2 phosphorylation was reduced in CM treated H9c2 cells, and inhibition of ERK 1/2 reduced the phosphorylation of Akt (Ser473), Akt (Thr308) and Bad (Ser112). In conclusion, MSC synthesize and secrete multiple paracrine factors that are able to affect MSC migration, promote angiogenesis and reduce apoptosis. While both MCP-1 and PI3-kinase are involved in the protective effect, they are independent of each other. It is likely that multiple pro-survival factors in addition to MCP-1 are secreted by MSC which act on divergent intracellular signaling pathways

Measurement of the cross-section of high transverse momentum vector bosons reconstructed as single jets and studies of jet substructure in pp collisions at √s = 7 TeV with the ATLAS detector

This paper presents a measurement of the cross-section for high transverse momentum W and Z bosons produced in pp collisions and decaying to all-hadronic final states. The data used in the analysis were recorded by the ATLAS detector at the CERN Large Hadron Collider at a centre-of-mass energy of √s = 7 TeV;{\rm Te}{\rm V}$and correspond to an integrated luminosity of$4.6\;{\rm f}{{{\rm b}}^{-1}}$. The measurement is performed by reconstructing the boosted W or Z bosons in single jets. The reconstructed jet mass is used to identify the W and Z bosons, and a jet substructure method based on energy cluster information in the jet centre-of-mass frame is used to suppress the large multi-jet background. The cross-section for events with a hadronically decaying W or Z boson, with transverse momentum${{p}_{{\rm T}}}\gt 320\;{\rm Ge}{\rm V}$and pseudorapidity$|\eta |\lt 1.9$, is measured to be${{\sigma }_{W+Z}}=8.5\pm 1.7$ pb and is compared to next-to-leading-order calculations. The selected events are further used to study jet grooming techniques