On the Non-invasive Measurement of the Intrinsic Quantum Hall Effect

With a model calculation, we demonstrate that a non-invasive measurement of intrinsic quantum Hall effect defined by the local chemical potential in a ballistic quantum wire can be achieved with the aid of a pair of voltage leads which are separated by potential barriers from the wire. B\"uttiker's formula is used to determine the chemical potential being measured and is shown to reduce exactly to the local chemical potential in the limit of strong potential confinement in the voltage leads. Conditions for quantisation of Hall resistance and measuring local chemical potential are given.Comment: 16 pages LaTex, 2 post-script figures available on reques

Backward error analysis and the substitution law for Lie group integrators

Butcher series are combinatorial devices used in the study of numerical methods for differential equations evolving on vector spaces. More precisely, they are formal series developments of differential operators indexed over rooted trees, and can be used to represent a large class of numerical methods. The theory of backward error analysis for differential equations has a particularly nice description when applied to methods represented by Butcher series. For the study of differential equations evolving on more general manifolds, a generalization of Butcher series has been introduced, called Lie--Butcher series. This paper presents the theory of backward error analysis for methods based on Lie--Butcher series.Comment: Minor corrections and additions. Final versio

A photonic basis for deriving nonlinear optical response

Nonlinear optics is generally first presented as an extension of conventional optics. Typically the subject is introduced with reference to a classical oscillatory electric polarization, accommodating correction terms that become significant at high intensities. The material parameters that quantify the extent of the nonlinear response are cast as coefficients in a power series - nonlinear optical susceptibilities signifying a propensity to generate optical harmonics, for example. Taking the subject to a deeper level requires a more detailed knowledge of the structure and properties of each nonlinear susceptibility tensor, the latter differing in form according to the process under investigation. Typically, the derivations involve intricate development based on time-dependent perturbation theory, assisted by recourse to a set of Feynman diagrams. This paper presents a more direct route to the required results, based on photonic rather than semiclassical principles, and offers a significantly clearer perspective on the photophysics underlying nonlinear optical response. The method, here illustrated by specific application to harmonic generation and down-conversion processes, is simple, intuitive and readily amenable for processes of arbitrary photonic order. © 2009 IOP Publishing Ltd

Thermo-Electric Properties of Quantum Point Contacts

I. Introduction II. Theoretical background (Landauer-Buttiker formalism of thermo-electricity, Quantum point contacts as ideal electron waveguides, Saddle-shaped potential) III. Experiments (Thermopower, Thermal conductance, Peltier effect) IV. ConclusionsComment: #4 of a series of 4 legacy reviews on QPC'

Unsupervised machine learning of integrated health and social care data from the Macmillan Improving the Cancer Journey service in Glasgow

Background: Improving the Cancer Journey (ICJ) was launched in 2014 by Glasgow City Council and Macmillan Cancer Support. As part of routine service, data is collected on ICJ users including demographic and health information, results from holistic needs assessments and quality of life scores as measured by EQ-5D health status. There is also data on the number and type of referrals made and feedback from users on the overall service. By applying artificial intelligence and interactive visualization technologies to this data, we seek to improve service provision and optimize resource allocation.Method: An unsupervised machine-learning algorithm was deployed to cluster the data. The classical k-means algorithm was extended with the k-modes technique for categorical data, and the gap heuristic automatically identified the number of clusters. The resulting clusters are used to summarize complex data sets and produce three-dimensional visualizations of the data landscape. Furthermore, the traits of new ICJ clients are predicted by approximately matching their details to the nearest existing cluster center.Results: Cross-validation showed the model’s effectiveness over a wide range of traits. For example, the model can predict marital status, employment status and housing type with an accuracy between 2.4 to 4.8 times greater than random selection. One of the most interesting preliminary findings is that area deprivation (measured through Scottish Index of Multiple Deprivation-SIMD) is a better predictor of an ICJ client’s needs than primary diagnosis (cancer type).Conclusion: A key strength of this system is its ability to rapidly ingest new data on its own and derive new predictions from those data. This means the model can guide service provision by forecasting demand based on actual or hypothesized data. The aim is to provide intelligent person-centered recommendations. The machine-learning model described here is part of a prototype software tool currently under development for use by the cancer support community.Disclosure: Funded by Macmillan Cancer Support</p