We define valuations and dominance relations in torsion-free abelian groups and prove that they are essentially the same objects. Next we show that valuations correspond with ltrations of subgroups closed under division by integers. We also prove that every torsion-free abelian valued group can be embedded in the Hahn product of subgroups defined by the respective valuations. / En este trabajo definimos valoraciones y relaciones de dominación en grupos abelianos sin torsión y probamos que estos son esencialmente los mismos objetos. Adicionalmente probamos que las valoraciones también se corresponden con filtraciones de subgrupos cerrados por división por enteros y que todo grupo abeliano valorado y sin torsión puede sumergirse en el producto de Hahn de subgrupos definidos por la valoración.

This research address the problem of inferring, through Radio-Frequency Identification (RFID) tracking data, the graph structures underlying social interactions in a group of rhesus macaques (a species of monkey). These social interactions are considered as independent affiliative and dominative components and are characterized by a variety of visual and auditory displays and gestures. Social structure in a group is an important indicator of its members’ relative level of access to resources and has interesting implications for an individual’s health. Automatic inference of the social structure in an animal group enables a number of important capabilities, including: 1. A verifiable measure of how the social structure is affected by an intervention such as a change in the environment, or the introduction of another animal, and 2. A potentially significant reduction in person hours normally used for assessing these changes. The behaviors of interest in the context of this research are those definable using the macaques’ spatial (x,y,z) position and motion inside an enclosure. Periods of time spent in close proximity with other group members are considered to be events of passive interaction and are used in the calculation of an Affiliation Matrix. This represents the strength of undirected interaction or tie-strength between individual animals. Dominance is a directed relation that is quantified using a heuristic for the detection of withdrawal and displacement behaviors. The results of an analysis based on these approaches for a group of 6 male monkeys that were tracked over a period of 60 days at the Yerkes Primate Research Center are presented in this Thesis.