XtranX passenger: navegação inercial

Trabalho de Projecto para obtenção do grau de Mestre em Engenharia Informática e de Computadores

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.

How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?

Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable.

Spectral invariants of periodic nonautonomous discrete dynamical systems

For an interval map, the poles of the Artin-Mazur zeta function provide topological invariants which are closely connected to topological entropy. It is known that for a time-periodic nonautonomous dynamical system F with period p, the p-th power [zeta(F) (z)](p) of its zeta function is meromorphic in the unit disk. Unlike in the autonomous case, where the zeta function zeta(f)(z) only has poles in the unit disk, in the p-periodic nonautonomous case [zeta(F)(z)](p) may have zeros. In this paper we introduce the concept of spectral invariants of p-periodic nonautonomous discrete dynamical systems and study the role played by the zeros of [zeta(F)(z)](p) in this context. As we will see, these zeros play an important role in the spectral classification of these systems.

The insular shelves of the Faial-Pico Ridge (Azores archipelago): a morphological record of its evolution

Shelves surrounding reefless volcanic ocean islands are formed by surf erosion of their slopes during changing sea levels. Posterosional lava flows, if abundant, can cross the coastal cliffs and fill partially or completely the accommodation space left by erosion. In this study, multibeam bathymetry, high-resolution seismic reflection profiles, and sediment samples are used to characterize the morphology of the insular shelves adjacent to Pico Island. The data show offshore fresh lava flow morphologies, as well as an irregular basement beneath shelf sedimentary bodies and reduced shelf width adjacent to older volcanic edifices in Pico. These observations suggest that these shelves have been significantly filled by volcanic progradation and can thus be classified as rejuvenated. Despite the general volcanic infilling of the shelves around Pico, most of their edges are below the depth of the Last Glacial Maximum, revealing that at least parts of the island have subsided after the shelves formed by surf erosion. Prograding lava deltas reached the shelf edge in some areas triggering small slope failures, locally decreasing the shelf width and depth of their edges. These areas can represent a significant risk for the local population; hence, their identification can be useful for hazard assessment and contribute to wiser land use planning. Shelf and subaerial geomorphology, magnetic anomalies and crustal structure data of the two islands were also interpreted to reconstruct the long-term combined onshore and offshore evolution of the Faial-Pico ridge. The subaerial emergence of this ridge is apparently older than previously thought, i.e., before approximate to 850 ka.

Text classification using compression-based dissimilarity measures

Arguably, the most difficult task in text classification is to choose an appropriate set of features that allows machine learning algorithms to provide accurate classification. Most state-of-the-art techniques for this task involve careful feature engineering and a pre-processing stage, which may be too expensive in the emerging context of massive collections of electronic texts. In this paper, we propose efficient methods for text classification based on information-theoretic dissimilarity measures, which are used to define dissimilarity-based representations. These methods dispense with any feature design or engineering, by mapping texts into a feature space using universal dissimilarity measures; in this space, classical classifiers (e.g. nearest neighbor or support vector machines) can then be used. The reported experimental evaluation of the proposed methods, on sentiment polarity analysis and authorship attribution problems, reveals that it approximates, sometimes even outperforms previous state-of-the-art techniques, despite being much simpler, in the sense that they do not require any text pre-processing or feature engineering.

Spectral and dynamical invariants in a complete clustered network

The main result of this work is a new criterion for the formation of good clusters in a graph. This criterion uses a new dynamical invariant, the performance of a clustering, that characterizes the quality of the formation of clusters. We prove that the growth of the dynamical invariant, the network topological entropy, has the effect of worsening the quality of a clustering, in a process of cluster formation by the successive removal of edges. Several examples of clustering on the same network are presented to compare the behavior of other parameters such as network topological entropy, conductance, coefficient of clustering and performance of a clustering with the number of edges in a process of clustering by successive removal.