Abstract
Predictive modelling is a process used in predictive analytics to create a statistical model of future behaviour. Predictive analytics is the area of data mining concerned with forecasting probabilities and trends. On the other hand, Artificial Intelligence (AI) concerns itself with intelligent behaviour, i.e. the things that make us seem intelligent. Following this process of thinking, in this work the main goal is the assessment of the impact of using AI based tools for the development of intelligent predictive models, in particular those that may be used to establish the conditions in which the levels of manganese and turbidity in water supply are high. Indeed, one of the main problems that the water treatment plant at Monte Novo (in Evora, Portugal) uncovers is the appearance of high levels of manganese and turbidity in treated water, which sometimes exceed the parametric values established in Portuguese Law, respectively 50 mu g dm(-3) and 4 NTU. In this study we tried to find answers to the above problem by building predictive models. The models we developed shall enable the prediction of manganese and turbidity levels in treated water, in order to ensure that the water supply does not affect public health in a negative way and obeys the current legislation. The software used in this study was the Clementine 11.1. The C5.0 Algorithm was also used as a means of introducing Decision Trees and the K-Means Algorithm was used to construct clustering models. The data in the database was collected from 2005 to 2006 and includes reservoir water quality data, treated water data and volumes of water stored in the reservoir.

Abstract
The Theory of Planned Behavior studies the decision-making mechanisms of individuals. We construct a game theoretical model to understand the role of leaders in decision-making of individuals or groups.We study the characteristics of the leaders that can have a positive or negative influence over others’ behavioral decisions. © Springer-Verlag Berlin Heidelberg 2011.

Abstract
Given C-2 infinitely renormalizable unimodal maps f and g with a quadratic critical point and the same bounded combinatorial type, we prove that they are C1+alpha conjugate along the closure of the corresponding forward orbits of the critical points, for some alpha > 0.

Abstract
Recently, the notion of a reinfection threshold in epidemiological models of only partial immunity has been debated in the literature. We present a rigorous analysis of a model of reinfection which shows a clear threshold behaviour at the parameter point where the reinfection threshold was originally described. Furthermore, we demonstrate that this threshold is the mean field version of a transition in corresponding spatial models of immunization. The reinfection threshold corresponds to the transition between annular growth of an epidemics spreading into a susceptible area leaving recovered behind and compact growth of a susceptible-infected-susceptible region growing into a susceptible area. This transition between annular growth and compact growth was described in the physics literature long before the reinfection threshold debate broke out in the theoretical biology literature.

Abstract
We review some recent results concerning a connection between focal decomposition, renormalization and semiclassical physics. The dynamical behaviour of a family of mechanical systems which includes the pendulum at small neighbourhoods of the equilibrium but after long intervals of time can be characterized through a renormalization scheme acting on the dynamics of this family. We have proved that the asymptotic limit of this renormalization scheme is universal: it is the same for all the elements in the considered class of mechanical systems. As a consequence, we have obtained an asymptotic universal focal decomposition for this family of mechanical systems which can now be used to compute estimates for propagators in semiclassical physics.

Abstract
For the spatial stochastic susceptible-infected-susceptible model, we consider the perturbative series expansion of the gap between the dominant and subdominant eigenvalues of the evolution operator. We compute explicitly the first terms of the series expansion of the gap with difference equations for the calculation of states.