Voronoi cells via linear inequality systems

The theory and methods of linear algebra are a useful alternative to those of convex geometry in the framework of Voronoi cells and diagrams, which constitute basic tools of computational geometry. As shown by Voigt and Weis in 2010, the Voronoi cells of a given set of sites T, which provide a tesselation of the space called Voronoi diagram when T is finite, are solution sets of linear inequality systems indexed by T. This paper exploits systematically this fact in order to obtain geometrical information on Voronoi cells from sets associated with T (convex and conical hulls, tangent cones and the characteristic cones of their linear representations). The particular cases of T being a curve, a closed convex set and a discrete set are analyzed in detail. We also include conclusions on Voronoi diagrams of arbitrary sets.

Research-action Methodology between Computer Science and Educational Psychology: a Multidisciplinary Approach

Computer science studies possess a strong multidisciplinary aptitude since most graduates do their professional work outside of a computing environment, in close collaboration with professionals from many different areas. However, the training offered in computer science studies lacks that multidisciplinary factor, focusing more on purely technical aspects. In this paper we present a novel experience where computer studies and educational psychology find a common ground and realistic working through laboratory practices. Specifically, the work enables students of computer science education the development of diagnosis support systems, with artificial intelligence techniques, which could then be used for future educational psychologists. The applications developed by computer science students are the creation of a model for the diagnosis of pervasive developmental disorders (PDD), sometimes also commonly called the autism spectrum disorders (ASD). The complexity of this diagnosis, not only by the exclusive characteristics of every person who suffers from it, but also by the large numbers of variables involved in it, requires very strong and close interdisciplinary participation. This work demonstrates that it is possible to intervene in a curricular perspective, in the university, to promote the development of interpersonal skills. What can be shown, in this way, is a methodology for interdisciplinary practices design and a guide for monitoring and evaluation. The results are very encouraging since we obtained significant differences in academic achievement between students who attended a course using the new methodology and those who did not use it.

Inclusion of immersive virtual learning environments and visual control systems to support the learning of students with Asperger syndrome

This paper presents the use of immersive virtual reality systems in the educational intervention with Asperger students. The starting points of this study are features of these students' cognitive style that requires an explicit teaching style supported by visual aids and highly structured environments. The proposed immersive virtual reality system, not only to assess the student's behavior and progress, but also is able to adapt itself to the student's specific needs. Additionally, the immersive reality system is equipped with sensors that can determine certain behaviors of the students. This paper determines the possible inclusion of immersive virtual reality as a support tool and learning strategy in these particular students' intervention. With this objective two task protocols have been defined with which the behavior and interaction situations performed by participant students are recorded. The conclusions from this study talks in favor of the inclusion of these virtual immersive environments as a support tool in the educational intervention of Asperger syndrome students as their social competences and executive functions have improved.

An alternative disjunctive optimization model for heat integration with variable temperatures

This paper presents an alternative model to deal with the problem of optimal energy consumption minimization of non-isothermal systems with variable inlet and outlet temperatures. The model is based on an implicit temperature ordering and the “transshipment model” proposed by Papoulias and Grossmann (1983). It is supplemented with a set of logical relationships related to the relative position of the inlet temperatures of process streams and the dynamic temperature intervals. In the extreme situation of fixed inlet and outlet temperatures, the model reduces to the “transshipment model”. Several examples with fixed and variable temperatures are presented to illustrate the model's performance.

Logic-Based Outer Approximation for the Design of Discrete-Continuous Dynamic Systems with Implicit Discontinuities

We address the optimization of discrete-continuous dynamic optimization problems using a disjunctive multistage modeling framework, with implicit discontinuities, which increases the problem complexity since the number of continuous phases and discrete events is not known a-priori. After setting a fixed alternative sequence of modes, we convert the infinite-dimensional continuous mixed-logic dynamic (MLDO) problem into a finite dimensional discretized GDP problem by orthogonal collocation on finite elements. We use the Logic-based Outer Approximation algorithm to fully exploit the structure of the GDP representation of the problem. This modelling framework is illustrated with an optimization problem with implicit discontinuities (diver problem).