Collaboration for Social Innovation: Developing Social Learning Spaces in the UK Higher Education

This paper concerns initial work on social innovation that investigates the role of collaboration as a catalyst for change applied in the context of social learning spaces in the United Kingdom‟ higher education. From a policy viewpoint the paper addresses the issue of social technologies as a means of social practice. Secondly, it focuses on the impact a whole system change process can have upon university students and staff in establishing social learning spaces. Thirdly, it tackles leadership and how this can be effectively utilised within the field under consideration. Reference to specific cases of British Universities regarding use of social learning spaces is made and emphasis is given on the role of collaboration in pursuing innovative ideas. Semi-structured interviews and collection of secondary data are the research methods used. Finally, suggestions on how social learning spaces could be further improved are highlighted

Polynomial solutions of the Knizhnik-Zamolodchikov equations and Schur-Weyl duality

An integral formula for the solutions of Knizhnik-Zamolodchikov (KZ) equation with values in an arbitrary irreducible representation of the symmetric group S_N is presented for integer values of the parameter. The corresponding integrals can be computed effectively as certain iterated residues determined by a given Young diagram and give polynomials with integer coefficients. The derivation is based on Schur-Weyl duality and the results of Matsuo on the original SU(n) KZ equation. The duality between the spaces of solutions with parameters m and -m is discussed in relation with the intersection pairing in the corresponding homology groups.Comment: 14 pages, reference adde

CMB Anisotropy in Compact Hyperbolic Universes I: Computing Correlation Functions

CMB anisotropy measurements have brought the issue of global topology of the universe from the realm of theoretical possibility to within the grasp of observations. The global topology of the universe modifies the correlation properties of cosmic fields. In particular, strong correlations are predicted in CMB anisotropy patterns on the largest observable scales if the size of the Universe is comparable to the distance to the CMB last scattering surface. We describe in detail our completely general scheme using a regularized method of images for calculating such correlation functions in models with nontrivial topology, and apply it to the computationally challenging compact hyperbolic spaces. Our procedure directly sums over images within a specified radius, ideally many times the diameter of the space, effectively treats more distant images in a continuous approximation, and uses Cesaro resummation to further sharpen the results. At all levels of approximation the symmetries of the space are preserved in the correlation function. This new technique eliminates the need for the difficult task of spatial eigenmode decomposition on these spaces. Although the eigenspectrum can be obtained by this method if desired, at a given level of approximation the correlation functions are more accurately determined. We use the 3-torus example to demonstrate that the method works very well. We apply it to power spectrum as well as correlation function evaluations in a number of compact hyperbolic (CH) spaces. Application to the computation of CMB anisotropy correlations on CH spaces, and the observational constraints following from them, are given in a companion paper.Comment: 27 pages, Latex, 11 figures, submitted to Phys. Rev. D, March 11, 199

The ‘Cube’ and the ‘Poppy Flower’: Participatory approaches for designing technology-enhanced learning spaces

This paper presents an alternative method for designing learning spaces that is driven by the input of its users. An exploratory study was undertaken at an English university with the aim of redesigning technology-enhanced learning spaces. Two provocative concepts were presented to the participants as concepts of future learning spaces. Through participatory design workshops, students and teachers reflected and discussed the values of technology and provided insight into how to effectively embed technology in learning space design. The findings provide a set of recommendations for how to integrate technology in learning spaces and present alternative designs for each given concept

Isometry groups of proper metric spaces

Given a locally compact Polish space X, a necessary and sufficient condition for a group G of homeomorphisms of X to be the full isometry group of (X,d) for some proper metric d on X is given. It is shown that every locally compact Polish group G acts freely on GxY as the full isometry group of GxY with respect to a certain proper metric on GxY, where Y is an arbitrary locally compact Polish space with (card(G),card(Y)) different from (1,2). Locally compact Polish groups which act effectively and almost transitively on complete metric spaces as full isometry groups are characterized. Locally compact Polish non-Abelian groups on which every left invariant metric is automatically right invariant are characterized and fully classified. It is demonstrated that for every locally compact Polish space X having more than two points the set of proper metrics d such that Iso(X,d) = {id} is dense in the space of all proper metrics on X.Comment: 24 page

Permutations of Massive Vacua

We discuss the permutation group G of massive vacua of four-dimensional gauge theories with N=1 supersymmetry that arises upon tracing loops in the space of couplings. We concentrate on superconformal N=4 and N=2 theories with N=1 supersymmetry preserving mass deformations. The permutation group G of massive vacua is the Galois group of characteristic polynomials for the vacuum expectation values of chiral observables. We provide various techniques to effectively compute characteristic polynomials in given theories, and we deduce the existence of varying symmetry breaking patterns of the duality group depending on the gauge algebra and matter content of the theory. Our examples give rise to interesting field extensions of spaces of modular forms.Comment: 44 pages, 1 figur