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.

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.

Multiplexing Sensory Molecules Map Protons Near Micellar Membranes

Hi-fi mapping: Multiplexing fluorescent sensors that simultaneously target proton concentration and polarity move to micellar nanospaces, self-regulate their positions, and report their pKa values and wavelengths, which are controlled by their local environments. Such sensory functions enable maps of proton gradients near micellar membranes to be drawn.

Subpixel interpolation architecture for multistandard video motion estimation

A new reconfigurable subpixel interpolation architecture for multistandard (e.g., MPEG-2, MPEG-4, H.264, and AVS) video motion estimation (ME) is presented. This exploits the mixed use of parallel and serial-input FIR filters to achieve high throughput rate and efficient silicon utilization. Silicon design studies show that this can be implemented using 34.8 × 10 3 gates with area and performance that compares very favorably with specific fixed solutions, e.g., for the H.264 standard alone. This can support SDTV and HDTV applications when implemented in 0.18 µm CMOS technology, with further performance enhancements achievable at 0.13 µm and below. © 2009 IEEE.

Risk factors for the introduction and within-herd transmission of Mycobacterium avium subspecies paratuberculosis (MAP) infection in 59 Irish dairy herds

Since 1994, Irish cattle have been exposed to greater risks of acquiring Mycobacterium avium subspecies paratuberculosis (MAP) infection as a consequence of the importation of over 70,000 animals from continental Europe. In recent years, there has been an increase in the number of reported clinical cases of paratuberculosis in Ireland. This study examines the prevalence of factors that promote the introduction and within-herd transmission of Mycobacterium avium subspecies paratuberculosis (MAP) on selected Irish dairy farms in the Cork region, and the association between these factors and the results of MAP screening tests on milk sock filter residue (MFR). A total of 59 dairy farms, selected using non-random methods but apparently free of endemic paratuberculosis, were enrolled into the study. A questionnaire was used to collect data about risk factors for MAP introduction and transmission. The MFR was assessed on six occasions over 24 months for the presence of MAP, using culture and immunomagnetic separation prior to polymerase chain reaction (IMS-PCR). Furthermore, blood samples from all entire male and female animals over one year of age in 20 herds were tested by ELISA. Eighteen (31%) farms had operated as closed herds since 1994, 28 (47%) had purchased from multiple sources and 14 (24%) had either direct or indirect (progeny) contact with imported animals. Milk and colostrum were mixed on 51% of farms, while 88% of farms fed pooled milk. Thirty (51%) herds tested negative to MFR culture and IMS-PCR, 12 (20%) were MFR culture positive, 26 (44%) were IMS-PCR positive and seven (12%) were both culture and IMS-PCR positive. The probability of a positive MFR culture was significantly associated with reduced attendance at calving, and with increased use of individual calf pens and increased (but not significantly) if multiple suckling was practised. There was poor agreement between MFR culture and MFR IMS-PCR results, but moderate agreement between MFR culture and ELISA test results. This study highlights a lack of awareness among Irish dairy farmers about the effect of inadequate biosecurity on MAP introduction. Furthermore, within-herd transmission will be facilitated by traditional calf rearing and waste management practices. The findings of viable MAP in the presence of known transmission factors in non-clinically affected herds could be a prelude to long-term problems for the Irish cattle and agri-business generally.