José Cláudio do Nascimento

Francisco Leonardo Bezerra Martins, José Cláudio do Nascimento

Several populational networks present complex topologies when implemented in evolutionary algorithms. A common feature of these topologies is the emergence of a power law. Power law behavior with different scaling factors can also be observed in genealogical networks, but we still can not satisfactorily describe its dynamics or its relation to population evolution over time. In this paper, we use an algorithm to measure the impact of individuals in several numerical populations and study its dynamics of evolution through nonextensive statistics. Like this, we show evidence that the observed emergence of power law has a dynamic behavior over time. This dynamic development can be described using a family of q-exponential distributions whose parameters are time-dependent and follow a specific pattern. We also show evidence that elitism significantly influences the power law scaling factors observed. These results imply that the different power law shapes and deviations observed in genealogical networks are static images of a time-dependent dynamic development that can be satisfactorily described using q-exponential distributions.

José Cláudio do Nascimento

This paper shows that the fuzzy temporal logic can model figures of thought to describe decision-making behaviors. In order to exemplify, some economic behaviors observed experimentally were modeled from problems of choice containing time, uncertainty and fuzziness. Related to time preference, it is noted that the subadditive discounting is mandatory in positive rewards situations and, consequently, results in the magnitude effect and time effect, where the last has a stronger discounting for earlier delay periods (as in, one hour, one day), but a weaker discounting for longer delay periods (for instance, six months, one year, ten years). In addition, it is possible to explain the preference reversal (change of preference when two rewards proposed on different dates are shifted in the time). Related to the Prospect Theory, it is shown that the risk seeking and the risk aversion are magnitude dependents, where the risk seeking may disappear when the values to be lost are very high.