Explicit series solution for a glucose-induced electrical activity model of pancreatic beta-cells

In this work, we present the explicit series solution of a specific mathematical model from the literature, the Deng bursting model, that mimics the glucose-induced electrical activity of pancreatic beta-cells (Deng, 1993). To serve to this purpose, we use a technique developed to find analytic approximate solutions for strongly nonlinear problems. This analytical algorithm involves an auxiliary parameter which provides us with an efficient way to ensure the rapid and accurate convergence to the exact solution of the bursting model. By using the homotopy solution, we investigate the dynamical effect of a biologically meaningful bifurcation parameter rho, which increases with the glucose concentration. Our analytical results are found to be in excellent agreement with the numerical ones. This work provides an illustration of how our understanding of biophysically motivated models can be directly enhanced by the application of a newly analytic method.

Transmedia storytelling e a construção de um universo participativo: estudo de caso do projeto “collider”

Dissertação apresentada à Escola Superior de Comunicação Social como parte dos requisitos para obtenção de grau de mestre em Audiovisual e Multimédia.

Tsunamigenic earthquakes in the Gulf of Cadiz: fault model and recurrence

The Gulf of Cadiz, as part of the Azores-Gibraltar plate boundary, is recognized as a potential source of big earthquakes and tsunamis that may affect the bordering countries, as occurred on 1 November 1755. Preparing for the future, Portugal is establishing a national tsunami warning system in which the threat caused by any large-magnitude earthquake in the area is estimated from a comprehensive database of scenarios. In this paper we summarize the knowledge about the active tectonics in the Gulf of Cadiz and integrate the available seismological information in order to propose the generation model of destructive tsunamis to be applied in tsunami warnings. The fault model derived is then used to estimate the recurrence of large earthquakes using the fault slip rates obtained by Cunha et al. (2012) from thin-sheet neotectonic modelling. Finally we evaluate the consistency of seismicity rates derived from historical and instrumental catalogues with the convergence rates between Eurasia and Nubia given by plate kinematic models.

Design and construction of tunnels in zones subjected to high convergences

The economic development of a region depends on the speed that people and goods can travel. The reduction of people and goods travel time can be achieved by planning smooth road layouts, which are obtained by crossing natural obstacles such as hills, by tunneling at great depths, and allowing the reduction of the road alignment length. The stress state in rock masses at such depths, either because of the overburden or due to the tectonic conditions of the rock mass induces high convergences of the tunnel walls. These high convergence values are incompatible with the supports structural performance installed in the excavation stabilization. In this article it is intended to evaluate and analyze some of the solutions already implemented in several similar geological and geotechnical situations, in order to establish a methodological principle for the design of the tunnels included in a highway section under construction in the region influenced by the Himalayas, in the state of Himachal Pradesh (India) and referenced by "four laning of Kiratpur to Ner Chowk section".

Geological and geotechnical surveys in tectonically active rock masses

The economic development of a region depends on the speed that people and goods can travel. The reduction of people and goods travel time can be achieved by planning smooth road layouts, which are obtained by crossing natural obstacles such as hills, by tunneling at great depths, and allowing the reduction of the road alignment length. The stress state in rock masses at such depths, either because of the overburden or due to the tectonic conditions of the rock mass induces high convergences of the tunnel walls. These high convergence values are incompatible with the supports structural performance installed in the excavation stabilization. In this article it is intended to evaluate and analyze some of the solutions already implemented in several similar geological and geotechnical situations, in order to establish a methodological principle for the design of the tunnels included in a highway section under construction in the region influenced by the Himalayas, in the state of Himachal Pradesh (India) and referenced by "four laning of Kiratpur to Ner Chowk section".

GLODS: Global and Local Optimization using Direct Search

Locating and identifying points as global minimizers is, in general, a hard and time-consuming task. Difficulties increase in the impossibility of using the derivatives of the functions defining the problem. In this work, we propose a new class of methods suited for global derivative-free constrained optimization. Using direct search of directional type, the algorithm alternates between a search step, where potentially good regions are located, and a poll step where the previously located promising regions are explored. This exploitation is made through the launching of several instances of directional direct searches, one in each of the regions of interest. Differently from a simple multistart strategy, direct searches will merge when sufficiently close. The goal is to end with as many direct searches as the number of local minimizers, which would easily allow locating the global extreme value. We describe the algorithmic structure considered, present the corresponding convergence analysis and report numerical results, showing that the proposed method is competitive with currently commonly used global derivative-free optimization solvers.