SU(N) Monopoles and Platonic Symmetry

We discuss the ADHMN construction for SU(N) monopoles and show that a particular simplification arises in studying charge N-1 monopoles with minimal symmetry breaking. Using this we construct families of tetrahedrally symmetric SU(4) and SU(5) monopoles. In the moduli space approximation, the SU(4) one-parameter family describes a novel dynamics where the monopoles never separate, but rather, a tetrahedron deforms to its dual. We find a two-parameter family of SU(5) tetrahedral monopoles and compute some geodesics in this submanifold numerically. The dynamics is rich, with the monopoles scattering either once or twice through octahedrally symmetric configurations.Comment: 14pp, RevTex, two figures made of six Postscript files. To appear in the Journal of Mathematical Physic

Octahedral and Dodecahedral Monopoles

It is shown that there exists a charge five monopole with octahedral symmetry and a charge seven monopole with icosahedral symmetry. A numerical implementation of the ADHMN construction is used to calculate the energy density of these monopoles and surfaces of constant energy density are displayed. The charge five and charge seven monopoles look like an octahedron and a dodecahedron respectively. A scattering geodesic for each of these monopoles is presented and discussed using rational maps. This is done with the aid of a new formula for the cluster decomposition of monopoles when the poles of the rational map are close together.Comment: uuencoded latex, 20 pages, 2 figures To appear in Nonlinearit

Monopoles from Rational Maps

The moduli space of charge k SU(2) BPS monopoles is diffeomorphic to the moduli space of degree k rational maps between Riemann spheres. In this note we describe a numerical algorithm to compute the monopole fields and energy density from the rational map. The results for some symmetric examples are presented.Comment: 8 pages, 2 figures. To appear in Phys. Lett.

Rational Maps, Monopoles and Skyrmions

We discuss the similarities between BPS monopoles and Skyrmions, and point to an underlying connection in terms of rational maps between Riemann spheres. This involves the introduction of a new ansatz for Skyrme fields. We use this to construct good approximations to several known Skyrmions, including all the minimal energy configurations up to baryon number nine, and some new solutions such as a baryon number seventeen Skyrme field with the truncated icosahedron structure of a buckyball. The new approach is also used to understand the low-lying vibrational modes of Skyrmions, which are required for quantization. Along the way we discover an interesting Morse function on the space of rational maps which may be of use in understanding the Sen forms on the monopole moduli spaces.Comment: 35pp including four figures, typos corrected, appearing in Nuclear Physics

Where is the evidence: realising the value of grey literature for public policy and practice

This paper discusses the ways in which the internet has profoundly changed how we produce, use and collect research and information for public policy and practice, particularly focusing on the benefits and challenges presented by grey literature. The authors argue that grey literature (i.e. material produced and published by organisations  without recourse to the commercial or scholarly publishing industry) is a key part of the evidence produced and used for public policy and practice. Through surveys of users, producing organisations and collecting services a detailed picture is provided of the role, importance and economic value of grey literature. However, finding and accessing policy information is a time-consuming task made harder by poor production and management of resources and a lack of large-scale collection services able to host and make available  relevant, high-quality resources quickly and efficiently. The paper makes recommendations for changes that would maximise the benefits of grey literature in the public interest and seeks feedback from readers to inform the final report of the research project. Public policy work increasingly relies on a wide range of resources — some are traditional scholarly publications, but the majority are ‘grey literature’. Reports, discussion papers, briefings, reviews and data sets produced by government, academic centres, NGOs, think tanks and companies are heavily used and highly valued in policy and practice work, forming a key part of the evidence base. The huge amount of information and research published online provides unprecedented access to knowledge, from a wide range of sources, enabling a much greater level of understanding and participation in public interest issues. It also brings a number of challenges: searching, sifting, evaluating and accessing information and research are time-consuming and often frustrating tasks occupying a large portion of the work hours of those engaged in policy work. Online publishing also creates a new paradigm for those whose task it is to support policy and practice work through effective resource provision and information management. As a result, digital curation of policy resources, particularly grey literature, is dispersed and fragmented, creating a digital black hole of resources that are lost from online access over time. The aim of the Grey Literature Strategies research project is to investigate grey literature’s role and importance in policy work and find ways to enhance its value. A key method used was online surveys of producers, users, and collectors of information and research for policy and practice, conducted during 2013

Seiberg-Witten theory, monopole spectral curves and affine Toda solitons

Using Seiberg-Witten theory it is known that the dynamics of N=2 supersymmetric SU(n) Yang-Mills theory is determined by a Riemann surface. In particular the mass formula for BPS states is given by the periods of a special differential on this surface. In this note we point out that the surface can be obtained from the quotient of a symmetric n-monopole spectral curve by its symmetry group. Known results about the Seiberg-Witten curves then implies that these monopoles are related to the Toda lattice. We make this relation explicit via the ADHMN construction. Furthermore, in the simplest case, that of two SU(2) monopoles, we find that the general two monopole solution is generated by an affine Toda soliton solution of the imaginary coupled theory.Comment: uuencoded latex, 15 pages, 1 figure. To appear in Physics Letters

Symmetric Instantons and Skyrme Fields

By explicit construction of the ADHM data, we prove the existence of a charge seven instanton with icosahedral symmetry. By computing the holonomy of this instanton we obtain a Skyrme field which approximates the minimal energy charge seven Skyrmion. We also present a one parameter family of tetrahedrally symmetric instantons whose holonomy gives a family of Skyrme fields which models a Skyrmion scattering process, where seven well-separated Skyrmions collide to form the icosahedrally symmetric Skyrmion.Comment: 22 pages plus 1 figure in GIF forma

Multi-soliton dynamics in the Skyrme model

We exhibit the dynamical scattering of multi-solitons in the Skyrme model for configurations with charge two, three and four. First, we construct maximally attractive configurations from a simple profile function and the product ansatz. Then using a sophisticated numerical algorithm, initially well-separated skyrmions in approximately symmetric configurations are shown to scatter through the known minimum energy configurations. These scattering events illustrate a number of similarities to BPS monopole configurations of the same charge. A simple modification of the dynamics to a dissipative regime, allows us to compute the minimal energy skyrmions for baryon numbers one to four to within a few percent.Comment: latex, 10 pages, plus 5 figures (as gif files

Where Is the Evidence? Realising the Value of Grey Literature for Public Policy & Practice, A Discussion Paper

The internet has profoundly changed how we produce, use and collect research and information for public policy and practice, with grey literature playing an increasingly important role. The authors argue that grey literature (i.e. material produced and published by organisations without recourse to the commercial or scholarly publishing industry) is a key part of the evidence produced and used for public policy and practice. Through surveys of users, producing organisations and collecting services a detailed picture is provided of the importance and economic value of grey literature. However, finding and accessing policy information is a time-consuming task made harder by poor production and management of resources and a lack of large-scale collection services able to host and make available relevant, high-quality resources quickly and efficiently. The paper makes recommendations for changes that would maximise the benefits of grey literature in the public interest and seeks feedback from readers to inform the final report of the research project

Cerebellar state estimation enables resilient coupling across behavioural domains

Cerebellar computations are necessary for fine behavioural control and may rely on internal models for estimation of behaviourally relevant states. Here, we propose that the central cerebellar function is to estimate how states interact with each other, and to use these estimates to coordinates extra-cerebellar neuronal dynamics underpinning a range of interconnected behaviours. To support this claim, we describe a cerebellar model for state estimation that includes state interactions, and link this model with the neuronal architecture and dynamics observed empirically. This is formalised using the free energy principle, which provides a dual perspective on a system in terms of both the dynamics of its physical—in this case neuronal—states, and the inferential process they entail. As a demonstration of this proposal, we simulate cerebellar-dependent synchronisation of whisking and respiration, which are known to be tightly coupled in rodents, as well as limb and tail coordination during locomotion. In summary, we propose that the ubiquitous involvement of the cerebellum in behaviour arises from its central role in precisely coupling behavioural domains