Stability of hyperbolic space under Ricci flow

We study the Ricci flow of initial metrics which are C^0-perturbations of the hyperbolic metric on H^n. If the perturbation is bounded in the L^2-sense, and small enough in the C^0-sense, then we show the following: In dimensions four and higher, the scaled Ricci harmonic map heat flow of such a metric converges smoothly, uniformly and exponentially fast in all C^k-norms and in the L^2-norm to the hyperbolic metric as time approaches infinity. We also prove a related result for the Ricci flow and for the two-dimensional conformal Ricci flow.Comment: 18 page

The Impacts of the Proposed EU-Libya Trade Agreement

The paper provides an overview of the potential social, economic and environmental impacts of an EU-Libya FTA as gauged by the EU-Libya Sustainability Impact Assessment (SIA). The main potential benefits to both the EU and Libya from the proposed trade agreement come from closer cooperation in the energy sector rather than from the economy-wide effects of reducing trade barriers. The agreement may also have significant adverse effects that need to be taken into account.EU; EU-Libya FTA; Libya FTA; EU FTA; Libya; Libya trade agreement; EU-Libya trade agreement; Libya trade; SIA; Sustainability Impact Assessment; impact assessment; trade impact assessment; EU SIA; Trade; SIA; Prud'homme; Dan Prud'homme; Dan Prudhomme; Prudhomme; Prud'homme

Machine learning at the nanoscale

Although scanning probe microscopy (SPM) techniques have allowed researchers to interact with the nanoscale for decades now, little improvement has been made to the incredibly manual, time consuming process of setting up, running, and analysing the results of these experiments, often arising due to the constantly varying shape of the probe apex. Unlike traditional computing methods, machine learning methods (with neural networks in particular) are considerably more capable of automating subjective tasks such as these, and we are only just beginning to explore the potential applications of this technology in SPM. In this thesis we explore a number of areas where machine learning could potentially massively change the way we go about SPM experimentation. We begin by discussing the history, theory, and experimental concepts of scanning tunnelling microscopy (STM), atomic force microscopy (AFM), and normal-incidence-x-ray standing wave (NIXSW). We then explore the makeup of a neural network and demonstrate how they can be applied to a variety of use-cases in SPM, including classification and policy prediction. Moving to the experimental chapters, we first discuss how we can successfully distinguish between STM tip states of the H:Si(100), Au(111) and Cu(111) surfaces. We also show that by adapting this network to work in real time, we improve performance while requiring on the order of 100x less data. We next discuss our attempts to combine these networks with expert examples to intelligently maintain tip apex sharpness during experimentation, envisioning an end-to-end automatic experiment. Because one of the main difficulties in applying machine learning is the frequent need to manually label data, we then show how we can use Monte Carlo simulations of self-organised AFM nanostructures to automatically label training data for a network, and then combine it with classical statistics and preprocessing to find specific structures in a mixed, messy dataset of real, experimental AFM images. As part of this, we also build a network to denoise experimental images. Finally, we present NIXSW results from an investigation into the temperature dependence of H20@C60, discussing the potential to use unsupervised clustering techniques to distinguish between noisy human-indistinguishable spectra to overcome limitations in data collection

High-speed AFM with a light touch

No abstract available

The Impacts of the Proposed EU-Libya Trade Agreement

The paper provides an overview of the potential social, economic and environmental impacts of an EU-Libya FTA as gauged by the EU-Libya Sustainability Impact Assessment (SIA). The main potential benefits to both the EU and Libya from the proposed trade agreement come from closer cooperation in the energy sector rather than from the economy-wide effects of reducing trade barriers. The agreement may also have significant adverse effects that need to be taken into account