Control Theory and Estimation
Control theory, developed by mathematicians in the 50s, has played a relevant role in the design and implementation of worldwide advances in areas of engineering, military, economics, finances, health, among others. Additionally, the understanding of nonlinear, non-Gaussian dynamic systems, complexities and simplifications has given way to theoretical developments, in terms of estimations of states and/or the parameters of the modeled systems, in order to intervene everything and reach conclusions. The PhD program in Mathematical Engineering pursues this line of research, making theoretical contributions from signal analysis theory, nonlinear systems and estimations in small and large dimensions. With such contributions, solutions obtained can be applied to real-life problems in the industry.
Wavelet analysis, integral transformations, Bayesian estimations, data assimilations, among others, are topics of research in this program. These topics can be applied to computational methods in applied mathematics, atmospheric modeling, seismic migration, epidemiological modeling, industrial automation, etc.
Artificial Intelligence
With the advent of the age of automation, the natural question arose about giving intelligence to machines, devices and tools in order to improve its ability to “reason” and therefore, perform better on tasks where human beings are experts and perform very accurately in. This idea brought about the emergence of new theories of sets and learning algorithms trying to represent the way in which the human being thinks and learns. In this line of research, we formulate questions that lead to the development of new theoretical and practical elements in supervised and unsupervised learning algorithms. The areas of interest of this line of research are fuzzy and local spectral clustering combined with extraction techniques of unstructured information; learning of the deep web (deep learning) with potential applications in information extraction in highly interconnected systems with weak connections and information processing and imaging.