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.

Superficialidad máxima. Superficie como posibilidad de sentido: imagen y síntoma

En estas páginas se pretende proponer un modo de entender lo visto siempre como adaptación inmanente, deseo y simbolización, esto es, entenderlo como imagen. Se hará conforme a un concepto de ‘superficie’ que prolonga la lectura que hiciera Didi-Huberman del concepto de imagen-síntoma de Aby Warburg, y se apoya en textos de teoría psicoanalítica de la mano de Jacques Lacan, en un intento no de arruinar la capacidad de hermenéutica del observador, sino de entender la búsqueda del sentido y de la esencia –del arte por ejemplo– como la investigación sobre un conflicto histórico de pérdidas, crisis y memoria. ‘Superficie’ en tanto que masa átona y sin sentido donde el ojo siempre visiona formas: ver superficie es que el ojo siempre adapte lo visto, deseando abrirlo visionariamente en su significado para recabar su verdad oculta, pero paradójicamente cerrándolo. Porque mirar imágenes supone siempre perder visión respecto de una supuesta totalidad en la que se darían todos los significados en todas sus ambigüedades y en todas sus posibilidades históricas, pérdida sólo decible en su retorno en tanto que resignificación traumática. Aquí postulamos que la ilusión será creer no que las apariencias son ilusorias, sino que más allá de ellas hay “más realidad”. Este planteamiento no sólo ratifica la posición del sujeto, inserto en una superficie/cuadro dada-a-ver, sino que descubre la brecha constitutiva que le rige y que es un “más en él” que él mismo.

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.

High-gain subwavelength resonant cavity antennas based on metamaterial ground planes

Planar metarnaterial Surfaces with negative reflection phase values are proposed as ground planes in a high-gain resonant cavity antenna configuration. The antenna is formed by the metarnaterial ground plane (MGP) and a superimposed metallodielectric electromagnetic band gap (MEBG) array that acts as a partially reflective surface (PRS). A single dipole positioned between the PRS and the ground IS utilised as the excitation. Ray analysis is employed to describe the functioning of the antennas and to qualitatively predict the effect of the MGP oil the antenna performance. By employing MGPs with negative reflection phase values, the planar antenna profile is reduced to subwavelength values (less than lambda/6) whilst maintaining high directivity. Full-wave simulations have been carried out with commercially available software (Microstripes (TM)). The effect of the finite PRS size on the antenna radiation performance (directivity and sidelobe level) is studied. A prototype has been fabricated and tested experimentally in order to validate the predictions.

Miniaturization of electromagnetic band gap structures for mobile applications

It is well known that interference of the human body affects the performance of the antennas in mobile phone handsets. In this contribution, we investigate the use of miniaturized metallodielectric electromagnetic band gap (MEBG) structures embedded in the case of a mobile handset as a means of decoupling the antenna from the user's hand. The closely coupled MEBG concept is employed to achieve miniaturization of the order of 15:1. Full wave dispersion relations for planar closely coupled MEBG arrays are presented and are validated experimentally. The performance of a prototype handset with an embedded conformal MEBG is assessed experimentally and is compared to a similar prototype without the MEBG. Reduction in the detuning of the antenna because of the human hand by virtue of the MEBG is demonstrated. Moreover, the efficiency of the handset when loaded with a human hand model is shown to improve when the MEBG is in place. The improvements are attributed to the decoupling of the antenna from the user's hand, which is achieved by means of suppressing the fields in the locality of the hand.

Efficient modelling technique for fractal electromagnetic band-gap arrays

An efficient modelling technique is proposed for the analysis of a fractal-element electromagnetic band-gap array. The modelling is based on a method of moments modal analysis in conjunction with an interpolation scheme, which significantly accelerates the computations. The plane-wave and the surface-wave responses of the structure have been studied by means of transmission coefficients and dispersion diagrams. The multiband properties and the compactness of the proposed structure are presented. The technique is general and can be applied to arbitrary-shaped element geometries.