Cartographic veracity in medieval mapping: analyzing geographical variation in the Gough Map of Great Britain

This article explores statistical approaches for assessing the relative accuracy of medieval mapping. It focuses on one particular map, the Gough Map of Great Britain. This is an early and remarkable example of a medieval “national” map covering Plantagenet Britain. Conventionally dated to c. 1360, the map shows the position of places in and coastal outline of Great Britain to a considerable degree of spatial accuracy. In this article, aspects of the map's content are subjected to a systematic analysis to identify geographical variations in the map's veracity, or truthfulness. It thus contributes to debates among historical geographers and cartographic historians on the nature of medieval maps and mapping and, in particular, questions of their distortion of geographic space. Based on a newly developed digital version of the Gough Map, several regression-based approaches are used here to explore the degree and nature of spatial distortion in the Gough Map. This demonstrates that not only are there marked variations in the positional accuracy of places shown on the map between regions (i.e., England, Scotland, and Wales), but there are also fine-scale geographical variations in the spatial accuracy of the map within these regions. The article concludes by suggesting that the map was constructed using a range of sources, and that the Gough Map is a composite of multiscale representations of places in Great Britain. The article details a set of approaches that could be transferred to other contexts and add value to historic maps by enhancing understanding of their contents.

Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.

The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius-Perron operator $U$ of the cusp map $F:[-1,1]\to [-1,1]$, $F(x)=1-2 x^{1/2}$ (which is an approximation of the Poincare section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in (0,1)$ the spectrum of $U$ in the Hardy space in the disk $\{z\in C:|z-q|

Extended spectral decompositions of the Renyi map

We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.

2.4 GHz Class-E power amplifier with transmissionline harmonic terminations

The design procedure, fabrication and measurement of a Class-E power amplifier with excellent second- and third-harmonic suppression levels are presented. A simplified design technique offering compact physical layout is proposed. With a 1.2 mm gate-width GaAs MESFET as a switching device, the amplifier is capable of delivering 19.2 dBm output power at 2.41 GHz, achieves peak PAE of 60% and drain efficiency of 69%, and exhibits 9 dB power gain when operated from a 3 V DC supply voltage. When compared to the classical Class-E two-harmonic termination amplifier, the Class-E amplifier employing three-harmonic terminations has more than 10% higher drain efficiency and 23 dB better third-harmonic suppression level. Experimental results are presented and good agreement with simulation is obtained. Further, to verify the practical implementation in communication systems, the Bluetooth-standard GFSK modulated signal is applied to both two- and three-harmonic amplifiers. The measured RMS FSK deviation error and RMS magnitude error were, for the three-harmonic case, 1.01 kHz and 0.122%, respectively, and, for the two-harmonic case, 1.09 kHz and 0.133%. © 2007 The Institution of Engineering and Technology.

A novel shrinkage technique based on the normal inverse Gaussian density model

This paper proposes a novel image denoising technique based on the normal inverse Gaussian (NIG) density model using an extended non-negative sparse coding (NNSC) algorithm proposed by us. This algorithm can converge to feature basis vectors, which behave in the locality and orientation in spatial and frequency domain. Here, we demonstrate that the NIG density provides a very good fitness to the non-negative sparse data. In the denoising process, by exploiting a NIG-based maximum a posteriori estimator (MAP) of an image corrupted by additive Gaussian noise, the noise can be reduced successfully. This shrinkage technique, also referred to as the NNSC shrinkage technique, is self-adaptive to the statistical properties of image data. This denoising method is evaluated by values of the normalized signal to noise rate (SNR). Experimental results show that the NNSC shrinkage approach is indeed efficient and effective in denoising. Otherwise, we also compare the effectiveness of the NNSC shrinkage method with methods of standard sparse coding shrinkage, wavelet-based shrinkage and the Wiener filter. The simulation results show that our method outperforms the three kinds of denoising approaches mentioned above.

A randomized controlled trial of tea tree oil (5%) body wash versus standard body wash to prevent colonization with methicillin-resistant Staphylococcus aureus (MRSA) in critically ill adults: research protocol

Background
Over the past ten years MRSA has become endemic in hospitals and is associated with increased healthcare costs. Critically ill patients are most at risk, in part because of the number of invasive therapies that they require in the intensive care unit (ICU). Washing with 5% tea tree oil (TTO) has been shown to be effective in removing MRSA on the skin. However, to date, no trials have evaluated the potential of TTO body wash to prevent MRSA colonization or infection. In addition, detecting MRSA by usual culture methods is slow. A faster method using a PCR assay has been developed in the laboratory, but requires evaluation in a large number of patients.

Methods/Design
This study protocol describes the design of a multicentre, phase II/III prospective open-label randomized controlled clinical trial to evaluate whether a concentration of 5% TTO is effective in preventing MRSA colonization in comparison with a standard body wash (Johnsons Baby Softwash) in the ICU. In addition we will evaluate the cost-effectiveness of TTO body wash and assess the effectiveness of the PCR assay in detecting MRSA in critically ill patients. On admission to intensive care, swabs from the nose and groin will be taken to screen for MRSA as per current practice. Patients will be randomly assigned to be washed with the standard body wash or TTO body wash. On discharge from the unit, swabs will be taken again to identify whether there is a difference in MRSA colonization between the two groups.

Discussion
If TTO body wash is found to be effective, widespread implementation of such a simple colonization prevention tool has the potential to impact on patient outcomes, healthcare resource use and patient confidence both nationally and internationally.

Trial Registration
[ISRCTN65190967]

Mapping the realm: A New Look at the Gough Map of Britain (c.1360)

The mid-fourteenth century map of Britain known as the ‘Gough’ map is the earliest extant depiction of the island in geographically recognizable form. Hitherto, however, interest in the road or route patterns marked on the map has meant that the map's extraordinarily rich settlement geography has not received the attention it merits and that, consequently, the point of the map may have been missed. The availability of a digital scan of the map coupled with the use of Geographical Information System (GIS) software provides the opportunity for a new look at the Gough map and the questions it poses. Attention in this article is directed to the settlement geography it shows, and in particular to the map's 654 cities, towns, villages, castles and monasteries. Their geographical positions as given on the manuscript are compared with their modern equivalents to shed light on some of the basic questions—the map's place of origin, the purpose or purposes for which it was made and the circumstances of its production—that have posed such a challenge for scholars. Our preliminary conclusion is that the key to understanding the original primary role of the Gough map lies in its accurate but selective depiction of the settlement geography of fourteenth-century Britain.