Persistence of fixed points under rigid perturbations of maps

Let $f:S^1\times [0,1]\to S^1\times [0,1]$ be a real-analytic annulus diffeomorphism which is homotopic to the identity map and preserves an area form. Assume that for some lift $\tilde {f}:\mathbb{R}\times [0,1]\rightarrow \mathbb{R}\times [0,1]$ we have ${\rm Fix}(\tilde{f})=\mathbb{R}\times \{0\}$ and that $\tilde{f}$ positively translates points in $\mathbb{R}\times \{1\}$. Let $\tilde{f}_\epsilon$ be the perturbation of $\tilde{f}$ by the rigid horizontal translation $(x,y)\mapsto (x+\epsilon,y)$. We show that for all $\epsilon >0$ sufficiently small we have ${\rm Fix} (\tilde{f}_\epsilon)=\emptyset$. The proof follows from Ker\'ekj\'art\'o's construction of Brouwer lines for orientation preserving homeomorphisms of the plane with no fixed points. This result turns out to be sharp with respect to the regularity assumption: there exists a diffeomorphism $f$ satisfying all the properties above, except that $f$ is not real-analytic but only smooth, so that the above conclusion is false. Such a map is constructed via generating functions

Dynamics of homeomorphisms of the torus homotopic to Dehn twists

In this paper we consider torus homeomorphisms $f$ homotopic to Dehn twists. We prove that if the vertical rotation set of $f$ is reduced to zero, then there exists a compact connected essential "horizontal" set K, invariant under $f$. In other words, if we consider the lift $\hat{f}$ of $f$ to the cylinder, which has zero vertical rotation number, then all points have uniformly bounded motion under iterates of $\hat{f}$. Also, we give a simple explicit condition which, when satisfied, implies that the vertical rotation set contains an interval and thus also implies positive topological entropy. As a corollary of the above results, we prove a version of Boyland's conjecture to this setting: If $f$ is area preserving and has a lift $\hat{f}$ to the cylinder with zero Lebesgue measure vertical rotation number, then either the orbits of all points are uniformly bounded under $\hat{f}$, or there are points in the cylinder with positive vertical velocity and others with negative vertical velocity

The transnational Gulf City: Saudi and migrant values of public open spaces in Jeddah

This paper outlines patterns of use, perceived benefits and place attachment relating to public open space in Jeddah, Saudi Arabia, a city in which almost half the residents are born overseas. The methods included case studies representing different recreational landscape typologies, observational analysis and 85 on-site interviews (46% Saudi, 54% migrants). The findings outline the benefits of visiting as a retreat from busy lifestyles, for everyday sociability, for improving health, for religious practice and for mutual support, highlighting dimensions of gender, transnationality and heritage. The paper explores place attachment related to displacement comparing between impacts of migration and of rapid urbanisation. The narratives suggest that experiences shaped by temporality and memory inform emotional geographies for both Saudi and migrant residents. There are differences in patterns of use between resident groups, but the paper concludes that, within a highly stratified society, the public open spaces of Jeddah provide an important resource of shared pleasures and everyday multiculture

The pair potential of colloidal stars

We report on the construction of colloidal stars: 1 micrometer polystyrene beads grafted with a dense brush of 1 micrometer long and 10 nm wide semi-flexible filamentous viruses. The pair interaction potentials of colloidal stars are measured using an experimental implementation of umbrella sampling, a technique originally developed in computer simulations in order to probe rare events. The influence of ionic strength and grafting density on the interaction is measured. Good agreements are found between the measured interactions and theoretical predictions based upon the osmotic pressure of counterions.Comment: 5 pages, 3 figures. Changed conten

Prevalence of transfusion-transmitted Chagas disease among multitransfused patients in Brazil

<p>Abstract</p> <p>Background</p> <p>Blood transfusion has always been an important route for Chagas Disease (CD) transmission. The high prevalence of CD in Latin America and its lifelong asymptomatic clinical picture pose a threat for the safety of the blood supply. The outcome of measures designed to improve transfusion safety can be assessed by evaluating the prevalence of CD among multitransfused patients</p> <p>Methods</p> <p>In order to assess the impact of CD control measures on the safety of the blood supply, an observational cross-sectional study was designed to determine the prevalence of CD in 351 highly transfused patients, in which vectorial transmission was excluded. This study compared patients that received transfusion products before (n = 230) and after (n = 121) 1997, when measures to control transfusion-transmitted CD were fully implemented in Brazil.</p> <p>Results</p> <p>The study group consisted of 351 patients exposed to high numbers of blood products during their lifetime (median number of units transfused = 51, range 10–2086). A higher prevalence of transfusion-transmitted CD (1.30%) was observed among multitransfused patients that received their first transfusion before 1997, compared with no cases of transfusion-transmitted CD among multitransfused patients transfused after that year. The magnitude of the exposure to blood products was similar among both groups (mean number of units transfused per year of exposure = 25.00 ± 26.46 and 23.99 ± 30.58 respectively; P = 0.75, Mann-Whitney test).</p> <p>Conclusion</p> <p>Multiple initiatives aimed to control vector and parental transmission of CD can significantly decrease transfusion-transmitted CD in Brazil. Our data suggest that mandatory donor screening for CD represents the most important measure to interrupt transmission of CD by blood transfusions.</p

Restoration of Contralateral Representation in the Mouse Somatosensory Cortex after Crossing Nerve Transfer

Avulsion of spinal nerve roots in the brachial plexus (BP) can be repaired by crossing nerve transfer via a nerve graft to connect injured nerve ends to the BP contralateral to the lesioned side. Sensory recovery in these patients suggests that the contralateral primary somatosensory cortex (S1) is activated by afferent inputs that bypassed to the contralateral BP. To confirm this hypothesis, the present study visualized cortical activity after crossing nerve transfer in mice through the use of transcranial flavoprotein fluorescence imaging. In naïve mice, vibratory stimuli applied to the forepaw elicited localized fluorescence responses in the S1 contralateral to the stimulated side, with almost no activity in the ipsilateral S1. Four weeks after crossing nerve transfer, forepaw stimulation in the injured and repaired side resulted in cortical responses only in the S1 ipsilateral to the stimulated side. At eight weeks after crossing nerve transfer, forepaw stimulation resulted in S1 cortical responses of both hemispheres. These cortical responses were abolished by cutting the nerve graft used for repair. Exposure of the ipsilateral S1 to blue laser light suppressed cortical responses in the ipsilateral S1, as well as in the contralateral S1, suggesting that ipsilateral responses propagated to the contralateral S1 via cortico-cortical pathways. Direct high-frequency stimulation of the ipsilateral S1 in combination with forepaw stimulation acutely induced S1 bilateral cortical representation of the forepaw area in naïve mice. Cortical responses in the contralateral S1 after crossing nerve transfer were reduced in cortex-restricted heterotypic GluN1 (NMDAR1) knockout mice. Functional bilateral cortical representation was not clearly observed in genetically manipulated mice with impaired cortico-cortical pathways between S1 of both hemispheres. Taken together, these findings strongly suggest that activity-dependent potentiation of cortico-cortical pathways has a critical role for sensory recovery in patients after crossing nerve transfer

Contributos para um plano estratégico para o turismo do Município de Castro Daire

Pretende-se com este estudo dar um contributo para a elaboração de um plano estratégico de desenvolvimento turístico do Município de Castro Daire, que possa constituir uma ferramenta de trabalho para os vários players do território Castrense. É apresentado um enquadramento dos conceitos chave (Plano Estratégico para o Desenvolvimento Turístico de Territórios, Turismo de Natureza e Turismo de Saúde e Bem-Estar) e efetuada uma análise estratégica que inclui 32 entrevistas realizadas a agentes conhecedores do setor do Turismo Castrense e 400 inquéritos aplicados na Bolsa de Turismo de Lisboa e na Feira Ibéria de Turismo. A análise estratégica efetuada permitiu identificar os fatores críticos de sucesso, mas também os pontos fortes e os pontos fracos do território, a nível Turístico, bem com elencar as oportunidades e as ameaças relativas ao setor, de que resultou uma matriz SWOT. A partir da análise estratégica é apresentada uma proposta com possíveis linhas orientadoras futuras, com vista à valorização sustentada do Território Castrense e ao impulsionamento da atividade turística, as quais assentam nos seus principais recursos endógenos, de que se destacam o Rio Paiva, a Serra do Montemuro, as Termas do Carvalhal, a Gastronomia Local, as Tradições, o Património e as Rotas Culturais.ABSTRACT: The aim of this study is to contribute for the elaboration of a strategic plan of Touristic development in the Municipality of Castro Daire that can become a working tool for the various players in the Castro Daire territory. It is presented a background for the key concepts (Strategic Plan for Touristic Development of Territories, Nature Tourism and Health and Wellness Tourism) and it is performed a strategic analysis that includes 32 interviews held with experts in the area of Tourism in Castro Daire and 400 surveys made in the Bolsa de Turismo de Lisboa (Lisbon Tourism Grant) and in Feira Ibérica de Turismo (Iberian Tourism Fair). The strategic analysis that was made has allowed to identify the critical success factors, but also the strong points and the weak points of the territory, on a Touristic level, as well as list the opportunities and the threats to the sector, from which arose a SWOT analysis. From the strategic analysis it is presented a proposal with possible future guidelines, aiming for a sustained appreciation of the Territory of Castro Daire and to boost the touristic activity, which is based on its main endogenous resources, out of which we can highlight the Paiva River, the Montemuro Mountain, the Carvalhal Thermal Spa, the Local Gastronomy, the Traditions, the Heritage and the Cultural Routes

HOMEOMORPHISMS OF THE ANNULUS WITH A TRANSITIVE LIFT II

Let f be a homeomorphism of the closed annulus A that preserves the orientation, the boundary components and that has a lift (f) over tilde to the in finite strip (A) over tilde which is transitive. We show that, if the rotation number of (f) over tilde restricted to both boundary components of A is strictly positive, then there exists a closed nonempty connected set Gamma subset of (A) over tilde such that Gamma subset of] - infinity,0] x [0,1], Gamma is unbounded, the projection of to Gamma A is dense, Gamma - (1, 0) subset of Gamma and (f) over tilde(Gamma) subset of Gamma. Also, if p(1) is the projection on the first coordinate of (A) over tilde, then there exists d > 0 such that, for any (z) over tilde is an element of Gamma, lim sup (n ->infinity) p(1)((f) over tilde (n) ((Z) over tilde)) - p(1) ((Z) over tilde)/n < -d.CNPq[304803/2006-5]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)CNPq[304360/2005-8