Ergodicity of polygonal slap maps

Polygonal slap maps are piecewise affine expanding maps of the interval obtained by projecting the sides of a polygon along their normals onto the perimeter of the polygon. These maps arise in the study of polygonal billiards with non-specular reflections laws. We study the absolutely continuous invariant probabilities of the slap maps for several polygons, including regular polygons and triangles. We also present a general method for constructing polygons with slap maps having more than one ergodic absolutely continuous invariant probability.Comment: 17 pages, 6 figure

Hyperbolic polygonal billiards with finitely many ergodic SRB measures

We study polygonal billiards with reflection laws contracting the reflected angle towards the normal. It is shown that if a polygon does not have parallel sides facing each other, then the corresponding billiard map has finitely many ergodic SRB measures whose basins cover a set of full Lebesgue measure.Comment: 26 pages, 2 figure

The role of the Ral/Exocyst pathway in structural plasticity at the Drosophila neuromuscular junction

ABSTRACT: Defects in synaptic morphology and activity-dependent plasticity are a hallmark of neurodevelopmental and neurodegenerative disorders. Neuronal structure is critical for determining the properties of neurons, yet very little is known about the membrane dynamics that controls synaptic morphology. It is therefore critical to know the basic mechanisms by which neurons acquire their shape and change it in response to activity. This capacity of response is called synaptic plasticity, and allows modifications to be made in both pre- and post- synaptic elements of the synaptic terminal and their synapses. Given that synaptic plasticity is key for neurons to adapt to stimuli, it is important to study and understand the mechanisms by which it occurs and how defects can affect function. In this study, using the Drosophila neuromuscular junction as model, we show that activity-dependent formation of new presynaptic boutons is compromised when Ral and exocyst function is impaired, suggesting that this pathway plays a central role in structural plasticity. Ral GTPase is a small GTPase from the Ras superfamily and the exocyst is a conserved protein complex that is an effector for several GTPases, which, collectively might serve to control where, when and how, are vesicles targeted to a specific exocytic place. Dissecting the signaling cascade triggered by the Ral/Exocyst pathway will be key to understand how intracellular trafficking participates in this form of plasticity.RESUMO: Alterações na morfologia sináptica e na plasticidade dependente de actividade têm sido um ponto crucial no estudo das perturbações no desenvolvimento neuronal e nas doenças neurodegenerativas. A estrutura neuronal é importante para definir as propriedades neuronais, no entanto pouco é sabido acerca de como a dinâmica membranar controla a morfologia sináptica. Deste modo, é necessário perceber os mecanismos básicos através dos quais os neurónios adquirem forma e de como a mudam em resposta a actividade. Esta capacidade de resposta é denominada de plasticidade sináptica e permite que sejam feitas modificações nos elementos pré- e pós- sinápticos dos terminais sinápticos e nas sinapses neles contidas. Sabendo que a plasticidade sináptica é um elemento chave na resposta dos neurónios a um estímulo, é importante estudar e perceber que mecanismos estão envolvidos e de que forma defeitos nesses mecanismos podem afectar a sua função. Neste estudo, recorrendo à junção neuromuscular de Drosophila melanogaster como modelo, é demonstrado que a formação de novos botões pré-sinápticos duma forma dependente de actividade é afectada quando existem defeitos na Ral ou no exocisto, sugerindo que a interacção entre estas proteínas é importante para a plasticidade estrutural. A Ral GTPase é uma pequena GTPase da superfamília das Ras GTPases, enquanto que o exocisto é um complexo proteico conservado que é um efetor de várias GTPases que pode controlar a maneira como as vesículas são exocitadas. Compreender a cascata de sinalização iniciada pela interacção entre a Ral e o exocisto poderá ser a chave para perceber como o tráfego intracelular participa neste tipo de plasticidade

Mineral waters, spas and therapeutics in seventeenth and eighteenth century Portugal

UID/HIS/04209/2013This article presents a general outline of the growing interest in medicinal waters and spas in Portugal during the eighteenth century, with special emphasis on the theoretical attitude and practice of the medical community and the ruling classes regarding mineral waters and on the development of the main institutions dedicated to hydrotherapy, trying to interpret the obstacles that prevented a more general social acceptance of spas and a greater adherence of physicians to therapeutic use of mineral waters in Portugal in this period.authorsversionpublishe

Near real-time analytics engine for vitals and environmental monitoring of first responders

First Responders are on a daily basis exposed to extreme conditions not only because of their duties but also due to the type of environment in which they perform. If the exposure to these conditions is not monitored, it may cause several health problems in long and short-term. This exposure can be controlled through vitals and environmental sensors placed in these professionals. However, the collected data is not relevant if it is not analyzed and processed. This analysis has the most benefits the closer it is to the moment the data is collected, allowing a more informed decision making. The purpose of this thesis is to study and implement a service system in the cloud enabling near real-time processing of the data that was collected by the sensors. This system allows the dynamic change of the running data processing services through a web interface, which also allows changing the source of the data that is going to be processed, whether it is from services that are external to the system or that are read directly from files. For this purpose we need each service to be sufficiently isolated not to interfere with others, choosing to keep a service per container because it addresses the least expensive virtualization option. This solution allows each machine to have several services that share the same computational resources, as its allocation is abstracted by the chosen solution. This system allows not only the integration of processing methods that already exist but also presents enough modularity so that they can be developed and integrated new methods

Renormalization of Gevrey vector fields with a Brjuno type arithmetical condition

We show that in the Gevrey topology,a d-torus flow close enough to linear with a unique rotation vector w is linearizable as long as w satisfies a novel Brjuno type Diophantine condition. The proof is based on the fast convergence under renormalization of the associated Gevrey vector field. It requires a multidimensional continued fractions expansion of w, and the corresponding characterization of the Brjuno type vectors.This demonstrates that renormalization methods deal very naturally with Gevrey regularity expressed in the decay of Fourier coefficients. In particular, they provide new linearization results including frequencies beyond Diophantine in non-analytic topologies.info:eu-repo/semantics/publishedVersio

Analysis of Lateral Displacements in Large Railway Viaducts Under Traffic Loads. Impact on Ride Safety and Passenger Comfort.

The increasing design speed of the new high speed lines and the stringent requirements on track alignment parameters are leading to a sustained increase of the number of railway viaducts. The relevant standards impose limiting values on lateral vibrations. Both the Spanish and European standards establish a minimum value for the first natural frequency of lateral vibration of a span, that should not be lower than fh0 = 1,2 Hz. This limit was originally proposed by ERRI committee D181, which assessed the lateral forces in railway bridges. This limit was proposed in order to avoid lateral resonance in railway vehicles going across the structure, taking into account that the frequencies of lateral vibration of railway vehicles are, in general, not greater than 1,0 Hz. In the case of large continuous viaducts with high piers, the lateral deformations occurring during a train pass-by can be significant and the natural frequencies of the first mode of vibration of the deck can be very low. In these cases it is not clear whether the required verifications must be applied to spans considered independently, to several successive spans or to the whole viaduct. There is currently no analysis methodology allowing to assess this situation and check the viaduct design against the requirements of ride safety and passenger comfort. This paper analyzes the lateral deformations of a large continuous viaduct and the infrastructure vehicle interaction effects due to the circulation of freight trains and several types of high speed train sat different speeds. The application of this methodology will allow an optimized design of viaducts with significant lateral deformations that cannot be justified only by using the simplified criteria of the current applicable standards. In such cases, the compliance with standards may lead to over dimensioning or in other cases to neglect the limits without the adequate verification of the proper infrastructure behavior once it has been commissioned. As it is the case for vertical deformations, for which the European standards require the assessment of dynamic effects, we stress the need for a dynamic analysis of the effects of lateral deformations in large railway viaducts