Diagonal Peg Solitaire

We study the classical game of peg solitaire when diagonal jumps are allowed. We prove that on many boards, one can begin from a full board with one peg missing, and finish with one peg anywhere on the board. We then consider the problem of finding solutions that minimize the number of moves (where a move is one or more jumps by the same peg), and find the shortest solution to the "central game", which begins and ends at the center. In some cases we can prove analytically that our solutions are the shortest possible, in other cases we apply A* or bidirectional search heuristics.Comment: 20 pages, 11 figure

A general theory of discrimination learning

One important component of learning is the ability to determine the correct conditions under which a rule should be applied. We review a number of systems that discover relevant conditions through a generalization process, and discuss some drawbacks of this approach. We then review an alternative approach to learning through discrimination, in which overly general rules are made more conservative when they lead to errors. Unlike generalization-based programs, a discrimination-based system is able to learn disjunctive rules, discover regularities in errorful data, recover from changes in the environment, and learn useful rules despite incomplete representations. We show how our theory of discrimination learning can be applied to the domains of concept attainment, strategy learning, first language acquisition, and cognitive development. Finally, we evaluate the theory along the dimensions of simplicity, generality, and fertility

A case study of shared memory and message passing : the triangle puzzle

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1995.Includes bibliographical references (p. 63-65).by Kevin A. Lew.M.S

Razonamiento regresivo en situaciones de resolución de problemas: un modelo multidimensional

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, leída el 20-10-20The increasing technological progress has highlighted the importance of problem-solving processes and skills connected to programming methods. Among them, backward reasoning is recognized as a critical issue in advanced mathematics education. This, together with the growing interest in recent years of game-based university education is at the base of this research project. Two objectives are established: on the one hand, to extend the epistemic model of backward reasoning, existing in the mathematical literature, to a cognitive and didactic one; on the other hand, to establish principles for the design of university teaching situations focused on backward reasoning. To reach these objectives, four design experiments using strategy games and mathematical problems are developed. These involved a total of 322 university students, from first year of bachelor to PhD, attending the Universidad Complutense de Madrid (Spain) and the Università di Torino (Italy). They are involved in scientific careers (Mathematics, Mathematics Engineering and Computer Science) and teacher training careers (future mathematics professors in secondary school)...El creciente progreso tecnológico ha puesto de relieve la importancia de los procesos de resolución de problemas y los conocimientos técnicos relacionados con los métodos de programación. Entre ellos, el razonamiento regresivo se reconoce como una cuestión crítica en la enseñanza de las matemáticas avanzada. Esto, junto con el creciente interés en los últimos años de la educación universitaria basada en juegos, es la base de esta investigación. Se establecen dos objetivos: 1) ampliar el modelo epistémico de razonamiento regresivo, existente en la literatura matemática, a uno cognitivo y didáctico, y 2) establecer principios para el diseño de situaciones de enseñanza universitaria centradas en el razonamiento regresivo. Para lograr estos objetivos, se desarrollan cuatro Design experiments utilizando juegos de estrategia y problemas matemáticos. En ellos participaron un total de 322 estudiantes universitarios, desde el primer año de grado hasta el doctorado, procedentes de la Universidad Complutense de Madrid (España) y de la Università di Torino (Italia). Son estudiantes de las ramas científica y de ingeniería (Matemáticas, Ingeniería Matemática e Informática) y en la especialidad de formación de profesores (futuros profesores de matemáticas en la escuela secundaria)...Fac. de Ciencias MatemáticasTRUEunpu

Emergent Behavior Development and Control in Multi-Agent Systems

Emergence in natural systems is the development of complex behaviors that result from the aggregation of simple agent-to-agent and agent-to-environment interactions. Emergence research intersects with many disciplines such as physics, biology, and ecology and provides a theoretical framework for investigating how order appears to spontaneously arise in complex adaptive systems. In biological systems, emergent behaviors allow simple agents to collectively accomplish multiple tasks in highly dynamic environments; ensuring system survival. These systems all display similar properties: self-organized hierarchies, robustness, adaptability, and decentralized task execution. However, current algorithmic approaches merely present theoretical models without showing how these models actually create hierarchical, emergent systems. To fill this research gap, this dissertation presents an algorithm based on entropy and speciation - defined as morphological or physiological differences in a population - that results in hierarchical emergent phenomena in multi-agent systems. Results show that speciation creates system hierarchies composed of goal-aligned entities, i.e. niches. As niche actions aggregate into more complex behaviors, more levels emerge within the system hierarchy, eventually resulting in a system that can meet multiple tasks and is robust to environmental changes. Speciation provides a powerful tool for creating goal-aligned, decentralized systems that are inherently robust and adaptable, meeting the scalability demands of current, multi-agent system design. Results in base defense, k-n assignment, division of labor and resource competition experiments, show that speciated populations create hierarchical self-organized systems, meet multiple tasks and are more robust to environmental change than non-speciated populations

Understanding human culture : theoretical and experimental studies of cumulative culture

There is something extraordinary about human culture. The striking complexity of our technologies, institutions, beliefs, and norms has allowed us to colonise the entire planet. One aspect in which human culture is unique relates to its cumulative nature – we accumulate and build on knowledge from the previous generations, leading to incremental improvement in skill, which allows us to produce technologies no one individual could have invented on their own. Understanding the drivers and dynamics of this type of cumulative culture is essential for understanding how human culture has interacted with human evolution. This thesis is concerned with precisely that, and uses a mixture of theoretical and experimental approaches linking individual-level decisions to population-level processes in cumulative culture contexts. Chapter 1 provides some essential background information. In Chapter 2 I used an agent-based simulation model to show that refinement, or incremental improvement in cultural traits, can lead to a drastic decrease of cultural diversity at the population level. This pattern was confirmed using experimental data from a collaborative programming competition in Chapter 3, where I showed that in a cumulative setting, the differential riskiness of copying and innovation drives participants to converge on very similar solutions, leading to a loss of cultural diversity. In Chapter 4 I explored individual differences in social learning strategies, finding considerable variation in how individuals rely on copying, with more successful individuals being more exploratory. I found that successful individuals had more influence on subsequent entries, which is consistent with a prestige bias. Finally, Chapter 5 addressed the link between group structure, diversity, and cumulative improvement. I found that larger groups accumulate more improvement than smaller groups, but smaller groups can also inhibit the convergence patterns we witnessed in larger groups, suggesting an optimal level of connectivity responsible for cumulative improvement