# Carlos Grandón

Projet COPRIN
INRIA - Sophia Antipolis
2004 Routes des Lucioles, BP 93
06902 Sophia Antipolis - France
Tel  : (+33) (0)4 92 38 77 66
Fax : (+33) (0)4 92 38 76 43
e-mail : carlos@grandon.cl

## Presentation

Hello!. My name is Carlos Grandón. I'm Engineer in Computer Sciences and I have a Master degree in Computer Sciences from Federico Santa María University (UTFSM). At present, I'm doing a PhD in the COPRIN project of the French National Institute for Research in Computer Science and Control (INRIA) in Sophia Antipolis.

I belong to the second generation of Chileans arrived to INRIA, in the framework of an international agreement between the National Commission for Scientific and Technological Research of Chile (CONICYT) and the INRIA - Sophia Antipolis research unit, which supports scholarships for superior studies in this center.

My thesis subject is solving systems of equations with uncertainties, and more specifically, solving distance equations systems when there are uncertainties in the measure of distances in one o more equations. My PhD advisor is Bertrand Neveu, who works on solving CSP (Constraint Satisfaction Problems) since 1992.

## Research

The subject of my thesis is to develop a methodology based on constraint programming for tackling uncertainty in Numeric CSP. In order to limit the research, we study the quadratic problems (the first step to the nonlinear problems), particularly, the systems of distance equations, since these have special characteristics that facilitate their study (continuity, symmetry, differentiation, among others).

### Research interests

My research interests are:

• Interval Arithmetic (Interval analysis).
• Techniques for solving Numeric CSPs.
• Tackling uncertainties in equations systems.
• Filtering and consistency in continuous domains.

### Problem Description

A more formal description of the problem is:

We have a set of n points in the real space, in principle, of two or three dimensions, and a set of m relations among them (distance between pairs of points). Knowing that we don't have the exact value of the distance between one or more pairs of points, but a little interval [a,b], we want to determine as precise as possible, the positions of the points in the space. Figure 1 and Figure 2 show a distance constraint between three points in a two dimensional space. Figure 1 shows the problem without uncertainty, whereas figure B shows the same problem when the distance is determined by an interval.

Figura 1: Problem without uncertainty

Figura 2: Problem with uncertainty

The first difficulty that we found when the problem has uncertainties, is the number of solutions. The uncertainty transforms solution points (ABC and ABC') into connected sets containing each an infinite number of solutions (shown in red color in the figure 2). There are an continuous of solutions to the problem in both sets (in addition these sets are nonconvex). The aim is to identify the sets (more precisely, the solution configurations) as precise as prossible, using convex sets.

## Publications

### Thesis

You can find here some resources and examples of my work.

### Mapa v1.0

Mapa (MA Petite Application) is a small program that allows one to display boxes in 2D and 3D. It was made to graphically show the results of the algorithm we use. Basically it is a Python script that uses VTK and TKinter to do interact the graphical interface with the user. It runs on Linux and the documentation is in Spanish, English and French. The right animation was completely made in Mapa.

Executable: Mapa-v1.0
Documentation español, english, français.

Lastest News!!!. I did some little changes for using Mapa in a Windows based Machine. The script is basically the same, but it needs some additional tools (like python and VTK compiled and installed on Windows). The good news is I have these tools. The bad news is you must install it on your windows machine.

Look my Readme in order to do it. You will need:

1. Python installer (I got it from http://www.python.org)
2. Vtk-python (I got it from http://mayavi.sourceforge.net)
3. vtkRenderingPythonTkWidgets.dll (It comes with the vtk-python installer)
4. Mapawin (of course, my program ;-)