In this project automated fuzzy regression methods, fuzzy clustering methods and forecasting methods are plied to econometric models and financial time series. Particularly, methos like: Bacht Least Squares, Recursive Bacth Least Squares, Modified Learning from Example and Combined Recursive Bacth Least Squares are considered for modeling Economy data which are usually model by tradional regression. Moreover, a fuzzy hybrid system for forecasting financial time series is investigated. The system is based on the automatic adjustment method auto.arima included in the forecast package for R. The system allows the inclusion of expert-criteria, i.e, the user can set up restrictions on the clustering based on a priori knowledge of the time series. This approach can be applied to any time series meeting the requirements of Seasonal Autoregressive Integrated Moving Average (SARIMA) models. .
Many phenomena occurring in real-life applications, e.g., in physics, finance, biology, biomechanics, are modeled by means of ordinary (ODEs) or partial (PDE) differential equations. The understanding of these differential equations is closely connected to the understanding of their physical meaning and the qualitative and quantitative behavior of their solutions. However, only the simplest ordinary and partial differential equations have closed form solutions, i.e., solutions, which can be expressed in terms of fundamental functions. Therefore, a numerical approximation is in most cases the only way to nd the solution. Due to the complexity of models or the accuracy needed, efficient algorithms have to be developed for numerical simulation. Moreover, the optimal control problem is even more computationally demanding. Thus, modern tools from numerical mathematics and scientific computing, along with careful investigation and exploitation of the problem structure, are required. In this project we deal with two real-life applications and develop the mathematical framework needed to efficiently simulate and solve the related control problem numerically, i.e., modeling, numerical analysis, implementation, etc. We focus on Musculoskeletal Modeling and Simulation in climbing and Crime Modeling.
The shallow water equations are hyperbolic partial differential equations (or parabolic if viscous shear is considered) that describe the flow below a pressure surface in a fluid. They are modeling fluid dynamics phenomena where the horizontal length scale is much greater than the vertical length scale, e.g., in the atmosphere and the oceans. Moreover, models of water reservoirs, lakes and rivers have been proposed in the literature; in particular methods to control the flow behavior to prevent the effects of floods.
Glyphosate is one of the herbicides used by the Colombian government to spray coca fields close to the Ecuadorian border. The sprays have been taking place for a number of years and have been more frequent since 2000 (when \"Plan Colombia\" started).
For being located at the equator, Ecuador is one of the most affected countries by the weakened ozone layer; as a consequence skin cancer has increased rapidly in the last years. According to a report of 2008: one person out of ten could suffer skin cancer in the next ten years. Usually, the diagnosis of this type of cancer is based on the growth/evolution analysis of the patient pigmented lesions or melanomas. A change on: symmetry, borders, color, size and specific dermatoscopy patterns as well as monitoring the lesions help in the diagnosis.
