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.

From cell death to embryo arrest: Mathematical models of human preimplantation embryo development

Human preimplantation embryos exhibit high levels of apoptotic cells and high rates of developmental arrest during the first week in vitro. The relation between the two is unclear and difficult to determine by conventional experimental approaches, partly because of limited numbers of embryos. We apply a mixture of experiment and mathematical modeling to show that observed levels of cell death can be reconciled with the high levels of embryo arrest seen in the human only if the developmental competence of embryos is already established at the zygote stage, and environmental factors merely modulate this. This suggests that research on improving in vitro fertilization success rates should move from its current concentration on optimizing culture media to focus more on the generation of a healthy zygote and on understanding the mechanisms that cause chromosomal and other abnormalities during early cleavage stages.

Failure of programmed cell death and differentiation as causes of tumors: some simple mathematical models.

Most models of tumorigenesis assume that the tumor grows by increased cell division. In these models, it is generally supposed that daughter cells behave as do their parents, and cell numbers have clear potential for exponential growth. We have constructed simple mathematical models of tumorigenesis through failure of programmed cell death (PCD) or differentiation. These models do not assume that descendant cells behave as their parents do. The models predict that exponential growth in cell numbers does sometimes occur, usually when stem cells fail to die or differentiate. At other times, exponential growth does not occur: instead, the number of cells in the population reaches a new, higher equilibrium. This behavior is predicted when fully differentiated cells fail to undergo PCD. When cells of intermediate differentiation fail to die or to differentiate further, the values of growth parameters determine whether growth is exponential or leads to a new equilibrium. The predictions of the model are sensitive to small differences in growth parameters. Failure of PCD and differentiation, leading to a new equilibrium number of cells, may explain many aspects of tumor behavior--for example, early premalignant lesions such as cervical intraepithelial neoplasia, the fact that some tumors very rarely become malignant, the observation of plateaux in the growth of some solid tumors, and, finally, long lag phases of growth until mutations arise that eventually result in exponential growth.

Proceedings of the Second American-Soviet Symposium on the Use of Mathematical Models to Optimize Water Quality Management, Bloomfield Hills, Michigan, USA, August 27-30, 1979 /

Mode of access: Internet.

Mathematical models in the social sciences

Mode of access: Internet.

Improvement of mathematical models for simulation of vehicle handling. Volume 6: programmers' guide for the driver module. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for vehicle handling. Volume 7: technical manual for the general simulation. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for vehicle handling. Volume 8: summary report. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for simulation of vehicle handling. Volume 1: user's guide for the five degree of freedom models. Final report.

Mode of access: Internet.

Improvement of mathematical models for simulation of vehicle handling. Volume 2: programmers' guide for the five degree of freedom models. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for vehicle handling. Volume 3: technical manual for the five-degree-of-freedom models. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for vehicle handling. Volume 4: users'guide for the general simulation. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for simulation of vehicle handling. Volume 5: programmers' guide for the vehicle model. Part I: documentation through subroutine IOUT. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for simulation of vehicle handling. Volume 5: programmers' guide for the vehicle model. Part 2: documentation for subroutines PRTDIC through KNMTC. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for simulation of vehicle handling. Volume 5: programmers' guide for the vehicle model. Part 3: documentation for subroutines SLPCLC through OUTPUT and a double precision listing. Final report.

National Highway Traffic Safety Administration, Washington, D.C.