Combinatorial Hopf algebras from renormalization

In this paper we describe the right-sided combinatorial Hopf structure of three Hopf algebras appearing in the context of renormalization in quantum field theory: the non-commutative version of the Fa\`a di Bruno Hopf algebra, the non-commutative version of the charge renormalization Hopf algebra on planar binary trees for quantum electrodynamics, and the non-commutative version of the Pinter renormalization Hopf algebra on any bosonic field. We also describe two general ways to define the associative product in such Hopf algebras, the first one by recursion, and the second one by grafting and shuffling some decorated rooted trees.Comment: 16 page

The complex process of scaling the integration of technology enhanced learning in mainstream classrooms

The early optimism for how technology might transform teaching and learning practices in mainstream school classrooms has long faded in many countries around the world. Whilst early research findings suggested that this was due to obvious barriers such as access to the technology itself, more recent attempts to scale student-access have illuminated other factors and provided a more sound theoretical foundation for us to understanding the processes and products of scaling educational technology innovations. This keynote will use findings from key projects and initiatives to highlight what is being learned – and how this might inform future endeavours to realise a more 21st century curriculum

Bridging knowing and proving in mathematics An essay from a didactical perspective

Text of a talk at the conference "Explanation and Proof in Mathematics: Philosophical and Educational Perspective" held in Essen in November 2006International audienceThe learning of mathematics starts early but remains far from any theoretical considerations: pupils' mathematical knowledge is first rooted in pragmatic evidence or conforms to procedures taught. However, learners develop a knowledge which they can apply in significant problem situations, and which is amenable to falsification and argumentation. They can validate what they claim to be true but using means generally not conforming to mathematical standards. Here, I analyze how this situation underlies the epistemological and didactical complexities of teaching mathematical proof. I show that the evolution of the learners' understanding of what counts as proof in mathematics implies an evolution of their knowing of mathematical concepts. The key didactical point is not to persuade learners to accept a new formalism but to have them understand how mathematical proof and statements are tightly related within a common framework; that is, a mathematical theory. I address this aim by modeling the learners' way of knowing in terms of a dynamic, homeostatic system. I discuss the roles of different semiotic systems, of the types of actions the learners perform and of the controls they implement in constructing or validating knowledge. Particularly with modern technological aids, this model provides a basis designing didactical situations to help learners bridge the gap between pragmatics and theory

Discovery and characterization of small molecules that target the Ral GTPase

The Ras-like GTPases RalA and B are important drivers of tumor growth and metastasis. Chemicals that block Ral function would be valuable as research tools and for cancer therapeutics. Here, we used protein structure analysis and virtual screening to identify drug-like molecules that bind a site on the GDP-form of Ral. Compounds RBC6, RBC8 and RBC10 inhibited Ral binding to its effector RalBP1, Ral-mediated cell spreading in murine fibroblasts and anchorage-independent growth of human cancer cell lines. Binding of RBC8 derivative BQU57 to RalB was confirmed by isothermal titration calorimetry, surface plasma resonance and 15N-HSQC NMR. RBC8 and BQU57 show selectivity for Ral relative to Ras or Rho and inhibit xenograft tumor growth similar to depletion of Ral by siRNA. Our results show the utility of structure-based discovery for development of therapeutics for Ral-dependent cancers

The pursuit of happiness: the social and scientific origins of Hans Selye’s natural philosophy of life

© The Author(s) 2012. Open access article.In 1956, Hans Selye tentatively suggested that the scientific study of stress could ‘help us to formulate a precise program of conduct’ and ‘teach us the wisdom to live a rich and meaningful life’. Nearly two decades later, Selye expanded this limited vision of social order into a full-blown philosophy of life. In Stress without Distress, first published in 1974, he proposed an ethical code of conduct designed to mitigate personal and social problems. Basing his arguments on contemporary understandings of the biological processes involved in stress reactions, Selye referred to this code as ‘altruistic egotism’. This article explores the origins and evolution of Selye’s ‘natural philosophy of life’, analysing the links between his theories and adjacent intellectual developments in biology, psychosomatic and psychosocial medicine, cybernetics and socio-biology, and situating his work in the broader cultural framework of modern western societies.Wellcome Trus

Energy Education Incentives: Evaluating the Impact of Consumer Energy Kits

Measuring the energy and environmental impact of residential energy education efforts is difficult. The E-Conservation residential energy management program uses consumer energy kits to document the impact of energy-efficient improvements. The consumer energy kit provides an incentive for individuals attending energy education workshop, helps consumers identify simple energy-saving technologies, and provides consumers with accessible energy-saving actions. As a result of consumers installing the compact fluorescent light bulbs and low flow showerheads in the energy kits, measureable savings in terms of annual energy savings, kilowatt hours, gallons of water used, and CO2 reduction are achieved

Teacher as learner: a personal reflection on a short course for South African university educators

Higher education is understood to play a critical role in ongoing processes of social transformation in post-apartheid South Africa through the production of graduates who are critical and engaged citizens. A key challenge is that institutions of higher education are themselves implicated in reproducing the very hierarchies they hope to transform. In this paper, I reflect critically on my experiences of a course aimed at transforming teaching through transforming teachers. In this paper, I foreground my own positionality as a white female educator as I draw on feminist theorising to reflect on my experiences as a learner in the Community, Self and Identity course. I suggest that we need to teach in ways that are more cognisant of the complexities of the constraints on personal freedom in the past if we are to contribute to the development of social justice in the future.IS

Energy Education Ideas that Work

Due to rising fuel prices, energy conservation is an area of considerable importance to consumers and researchers in the United States. This article discusses methods that North Carolina\u27s E-Conservation Program uses to reach and teach consumers about energy efficiency and conservation. This growing energy conservation initiative is the result of partnerships between the North Carolina Cooperative Extension Service, leading energy authorities, and local extension agents across the state

Methotrexate-mediated activation of an AMPK-CREB-dependent pathway: a novel mechanism for vascular protection in chronic systemic inflammation

Aims Premature cardiovascular events complicate chronic inflammatory conditions. Low-dose weekly methotrexate (MTX), the most widely used disease-modifying drug for rheumatoid arthritis (RA), reduces disease-associated cardiovascular mortality. MTX increases intracellular accumulation of adenosine monophosphate (AMP) and 5-aminoimidazole-4-carboxamide ribonucleotide which activates AMP-activated protein kinase (AMPK). We hypothesised that MTX specifically protects the vascular endothelium against inflammatory injury via induction of AMPK-regulated protective genes. Methods/results In the (NZW×BXSB)F1 murine model of inflammatory vasculopathy, MTX 1 mg/kg/week significantly reduced intramyocardial vasculopathy and attenuated end-organ damage. Studies of human umbilical vein endothelial cells (HUVEC) and arterial endothelial cells (HAEC) showed that therapeutically relevant concentrations of MTX phosphorylate AMPKαThr172, and induce cytoprotective genes including manganese superoxide dismutase (MnSOD) and haem oxygenase-1 (HO-1). These responses were preserved when HUVECs were pretreated with tumour necrosis factor-α to mimic dysfunctional endothelium. Furthermore, MTX protected against glucose deprivation-induced endothelial apoptosis. Mechanistically, MTX treatment led to cyclic AMP response element-binding protein (CREB)Ser133 phosphorylation, while AMPK depletion attenuated this response and the induction of MnSOD and HO-1. CREB siRNA inhibited upregulation of both cytoprotective genes by MTX, while chromatin immunoprecipitation demonstrated CREB binding to the MnSOD promoter in MTX-treated EC. Likewise, treatment of (NZW×BXSB)F1 mice with MTX enhanced AMPKαThr172 phosphorylation and MnSOD, and reduced aortic intercellular adhesion molecule-1 expression. Conclusions These data suggest that MTX therapeutically conditions vascular endothelium via activation of AMPK-CREB. We propose that this mechanism contributes to the protection against cardiovascular events seen in patients with RA treated with MTX