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.

Chromosome 9p21.3 is associated with early-onset coronary heart disease in the Irish population

Coronary heart disease (CHD) remains a leading cause of death across the world. A region on chromosome 9p21.3 has been recently reported to be associated with CHD. We evaluated 3 SNPs and 3 common haplotypes in the 9p21.3 region in 1494 individuals from 580 Irish families, where at least 1 member had early-onset (males

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.

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.

STAT3, p38 MAP Kinase and NF-{kappa}B Drive Unopposed Monocyte-dependent Fibroblast MMP-1 Secretion in Tuberculosis.

Tissue destruction characterizes infection with Mycobacterium tuberculosis (Mtb). Type I collagen provides the lung's tensile strength, is extremely resistant to degradation, but is cleaved by matrix metalloproteinase (MMP)-1. Fibroblasts potentially secrete quantitatively more MMP-1 than other lung cells. We investigated mechanisms regulating Mtb-induced collagenolytic activity in fibroblasts in vitro and in patients. Lung fibroblasts were stimulated with conditioned media from Mtb-infected monocytes (CoMTb). CoMTb induced sustained increased MMP-1 (74 versus 16 ng/ml) and decreased tissue inhibitor of metalloproteinase (TIMP)-1 (8.6 versus 22.3 ng/ml) protein secretion. CoMTb induced a 2.7-fold increase in MMP-1 promoter activation and a 2.5-fold reduction in TIMP-1 promoter activation at 24 hours (P = 0.01). Consistent with this, TIMP-1 did not co-localize with fibroblasts in patient granulomas. MMP-1 up-regulation and TIMP-1 down-regulation were p38 (but not extracellular signal–regulated kinase or c-Jun N-terminal kinase) mitogen-activated protein kinase–dependent. STAT3 phosphorylation was detected in fibroblasts in vitro and in tuberculous granulomas.STAT3 inhibition reduced fibroblast MMP-1 secretion by 60% (P = 0.046). Deletion of the MMP-1 promoter NF-B–binding site abrogated promoter induction in response to CoMTb. TNF-, IL-1ß, or Oncostatin M inhibition in CoMTb decreased MMP-1 secretion by 65, 63, and 25%, respectively. This cytokine cocktail activated the same signaling pathways in fibroblasts and induced MMP-1 secretion similar to that induced by CoMTb. This study demonstrates in a cellular model and in patients with tuberculosis that in addition to p38 and NF-B, STAT3 has a key role in driving fibroblast-dependent unopposed MMP-1 production that may be key in tissue destruction in patients.