Cooperative Multi-robot Patrolling: A study of distributed approaches based on mathematical models of game theory to protect infrastructures

El principio de Teoría de Juegos permite desarrollar modelos estocásticos de patrullaje multi-robot para proteger infraestructuras criticas. La protección de infraestructuras criticas representa un gran reto para los países al rededor del mundo, principalmente después de los ataques terroristas llevados a cabo la década pasada. En este documento el termino infraestructura hace referencia a aeropuertos, plantas nucleares u otros instalaciones. El problema de patrullaje se define como la actividad de patrullar un entorno determinado para monitorear cualquier actividad o sensar algunas variables ambientales. En esta actividad, un grupo de robots debe visitar un conjunto de puntos de interés definidos en un entorno en intervalos de tiempo irregulares con propósitos de seguridad. Los modelos de partullaje multi-robot son utilizados para resolver este problema. Hasta el momento existen trabajos que resuelven este problema utilizando diversos principios matemáticos. Los modelos de patrullaje multi-robot desarrollados en esos trabajos representan un gran avance en este campo de investigación. Sin embargo, los modelos con los mejores resultados no son viables para aplicaciones de seguridad debido a su naturaleza centralizada y determinista. Esta tesis presenta cinco modelos de patrullaje multi-robot distribuidos e impredecibles basados en modelos matemáticos de aprendizaje de Teoría de Juegos. El objetivo del desarrollo de estos modelos está en resolver los inconvenientes presentes en trabajos preliminares. Con esta finalidad, el problema de patrullaje multi-robot se formuló utilizando conceptos de Teoría de Grafos, en la cual se definieron varios juegos en cada vértice de un grafo. Los modelos de patrullaje multi-robot desarrollados en este trabajo de investigación se han validado y comparado con los mejores modelos disponibles en la literatura. Para llevar a cabo tanto la validación como la comparación se ha utilizado un simulador de patrullaje y un grupo de robots reales. Los resultados experimentales muestran que los modelos de patrullaje desarrollados en este trabajo de investigación trabajan mejor que modelos de trabajos previos en el 80% de 150 casos de estudio. Además de esto, estos modelos cuentan con varias características importantes tales como distribución, robustez, escalabilidad y dinamismo. Los avances logrados con este trabajo de investigación dan evidencia del potencial de Teoría de Juegos para desarrollar modelos de patrullaje útiles para proteger infraestructuras. ABSTRACT Game theory principle allows to developing stochastic multi-robot patrolling models to protect critical infrastructures. Critical infrastructures protection is a great concern for countries around the world, mainly due to terrorist attacks in the last decade. In this document, the term infrastructures includes airports, nuclear power plants, and many other facilities. The patrolling problem is defined as the activity of traversing a given environment to monitoring any activity or sensing some environmental variables If this activity were performed by a fleet of robots, they would have to visit some places of interest of an environment at irregular intervals of time for security purposes. This problem is solved using multi-robot patrolling models. To date, literature works have been solved this problem applying various mathematical principles.The multi-robot patrolling models developed in those works represent great advances in this field. However, the models that obtain the best results are unfeasible for security applications due to their centralized and predictable nature. This thesis presents five distributed and unpredictable multi-robot patrolling models based on mathematical learning models derived from Game Theory. These multi-robot patrolling models aim at overcoming the disadvantages of previous work. To this end, the multi-robot patrolling problem was formulated using concepts of Graph Theory to represent the environment. Several normal-form games were defined at each vertex of a graph in this formulation. The multi-robot patrolling models developed in this research work have been validated and compared with best ranked multi-robot patrolling models in the literature. Both validation and comparison were preformed by using both a patrolling simulator and real robots. Experimental results show that the multirobot patrolling models developed in this research work improve previous ones in as many as 80% of 150 cases of study. Moreover, these multi-robot patrolling models rely on several features to highlight in security applications such as distribution, robustness, scalability, and dynamism. The achievements obtained in this research work validate the potential of Game Theory to develop patrolling models to protect infrastructures.

The Learning of the Mathematical Models to Aid Decision Making in the High Level Engineering Schools?

At present, in the University curricula in most countries, the decision theory and the mathematical models to aid decision making is not included, as in the graduate program like in Doctored and Master´s programs. In the Technical School of High Level Agronomic Engineers of the Technical University of Madrid (ETSIA-UPM), the need to offer to the future engineers training in a subject that could help them to take decisions in their profession was felt. Along the life, they will have to take a lot of decisions. Ones, will be important and others no. In the personal level, they will have to take several very important decisions, like the election of a career, professional work, or a couple, but in the professional field, the decision making is the main role of the Managers, Politicians and Leaders. They should be decision makers and will be paid for it. Therefore, nobody can understand that such a professional that is called to practice management responsibilities in the companies, does not take training in such an important matter. For it, in the year 2000, it was requested to the University Board to introduce in the curricula an optional qualified subject of the second cycle with 4,5 credits titled " Mathematical Methods for Making Decisions ". A program was elaborated, the didactic material prepared and programs as Maple, Lingo, Math Cad, etc. installed in several IT classrooms, where the course will be taught. In the course 2000-2001 this subject was offered with a great acceptance that exceeded the forecasts of capacity and had to be prepared more classrooms. This course in graduate program took place in the Department of Applied Mathematics to the Agronomic Engineering, as an extension of the credits dedicated to Mathematics in the career of Engineering.

Multidisciplinary Learning, Another way of Teaching Maths in Engineering

Multidisciplinary training is widely appreciated in industry and business, and nevertheless usually is not addressed in the early stages of most undergraduate programs. We outline here a multidisciplinary course for undergraduates studying engineering in which mathematics would be the common language, the transverse tool. The goal is motivating students to learn more mathematics and as a result, improve the quality of engineering education. The course would be structured around projects in four branches in engineering: mechanical, electrical, civil and bio-tech. The projects would be chosen among a wide variety of topics in engineering practice selected with the guidance of professional engineers. In these projects mathematics should interact with at least two other basic areas of knowledge in engineering: chemistry, computers science, economics, design or physics.

An example of Learning based on competences: Use of Maxima in Linear Algebra for Engineers

This paper analyzes the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is defined as an indicator of the generic ompetence: Use of Technology. Additionally, we show that using CAS could help to enhance the following generic competences: Self Learning, Planning and Organization, Communication and Writing, Mathematical and Technical Writing, Information Management and Critical Thinking.

Learning and Assessing Competencies: New challenges for Mathematics in Engineering Degrees in Spain.

The introduction of new degrees adapted to the European Area of Higher Education (EAHE) has involved a radically different approach to the curriculum. The new programs are structured around competencies that should be acquired. Considering the competencies, teachers must define and develop learning objectives, design teaching methods and establish appropriate evaluation systems. While most Spanish universities have incorporated methodological innovations and evaluation systems different from traditional exams, there is enough confusion about how to teach and assess competencies and learning outcomes, as traditionally the teaching and assessment have focused on knowledge. In this paper we analyze the state-of-the-art in the mathematical courses of the new engineering degrees in some Spanish universities.

Machine Learning in Scientometrics

El aprendizaje automático y la cienciometría son las disciplinas científicas que se tratan en esta tesis. El aprendizaje automático trata sobre la construcción y el estudio de algoritmos que puedan aprender a partir de datos, mientras que la cienciometría se ocupa principalmente del análisis de la ciencia desde una perspectiva cuantitativa. Hoy en día, los avances en el aprendizaje automático proporcionan las herramientas matemáticas y estadísticas para trabajar correctamente con la gran cantidad de datos cienciométricos almacenados en bases de datos bibliográficas. En este contexto, el uso de nuevos métodos de aprendizaje automático en aplicaciones de cienciometría es el foco de atención de esta tesis doctoral. Esta tesis propone nuevas contribuciones en el aprendizaje automático que podrían arrojar luz sobre el área de la cienciometría. Estas contribuciones están divididas en tres partes: Varios modelos supervisados (in)sensibles al coste son aprendidos para predecir el éxito científico de los artículos y los investigadores. Los modelos sensibles al coste no están interesados en maximizar la precisión de clasificación, sino en la minimización del coste total esperado derivado de los errores ocasionados. En este contexto, los editores de revistas científicas podrían disponer de una herramienta capaz de predecir el número de citas de un artículo en el fututo antes de ser publicado, mientras que los comités de promoción podrían predecir el incremento anual del índice h de los investigadores en los primeros años. Estos modelos predictivos podrían allanar el camino hacia nuevos sistemas de evaluación. Varios modelos gráficos probabilísticos son aprendidos para explotar y descubrir nuevas relaciones entre el gran número de índices bibliométricos existentes. En este contexto, la comunidad científica podría medir cómo algunos índices influyen en otros en términos probabilísticos y realizar propagación de la evidencia e inferencia abductiva para responder a preguntas bibliométricas. Además, la comunidad científica podría descubrir qué índices bibliométricos tienen mayor poder predictivo. Este es un problema de regresión multi-respuesta en el que el papel de cada variable, predictiva o respuesta, es desconocido de antemano. Los índices resultantes podrían ser muy útiles para la predicción, es decir, cuando se conocen sus valores, el conocimiento de cualquier valor no proporciona información sobre la predicción de otros índices bibliométricos. Un estudio bibliométrico sobre la investigación española en informática ha sido realizado bajo la cultura de publicar o morir. Este estudio se basa en una metodología de análisis de clusters que caracteriza la actividad en la investigación en términos de productividad, visibilidad, calidad, prestigio y colaboración internacional. Este estudio también analiza los efectos de la colaboración en la productividad y la visibilidad bajo diferentes circunstancias. ABSTRACT Machine learning and scientometrics are the scientific disciplines which are covered in this dissertation. Machine learning deals with the construction and study of algorithms that can learn from data, whereas scientometrics is mainly concerned with the analysis of science from a quantitative perspective. Nowadays, advances in machine learning provide the mathematical and statistical tools for properly working with the vast amount of scientometrics data stored in bibliographic databases. In this context, the use of novel machine learning methods in scientometrics applications is the focus of attention of this dissertation. This dissertation proposes new machine learning contributions which would shed light on the scientometrics area. These contributions are divided in three parts: Several supervised cost-(in)sensitive models are learned to predict the scientific success of articles and researchers. Cost-sensitive models are not interested in maximizing classification accuracy, but in minimizing the expected total cost of the error derived from mistakes in the classification process. In this context, publishers of scientific journals could have a tool capable of predicting the citation count of an article in the future before it is published, whereas promotion committees could predict the annual increase of the h-index of researchers within the first few years. These predictive models would pave the way for new assessment systems. Several probabilistic graphical models are learned to exploit and discover new relationships among the vast number of existing bibliometric indices. In this context, scientific community could measure how some indices influence others in probabilistic terms and perform evidence propagation and abduction inference for answering bibliometric questions. Also, scientific community could uncover which bibliometric indices have a higher predictive power. This is a multi-output regression problem where the role of each variable, predictive or response, is unknown beforehand. The resulting indices could be very useful for prediction purposes, that is, when their index values are known, knowledge of any index value provides no information on the prediction of other bibliometric indices. A scientometric study of the Spanish computer science research is performed under the publish-or-perish culture. This study is based on a cluster analysis methodology which characterizes the research activity in terms of productivity, visibility, quality, prestige and international collaboration. This study also analyzes the effects of collaboration on productivity and visibility under different circumstances.