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Abstract(s)
A Lei de PotĂȘncia Ă© uma particularidade de um sistema nĂŁo linear, revelando um sistema complexo prĂłximo da auto-organização. Algumas caracterĂsticas de sistemas naturais e artificiais, tais como dimensĂŁo populacional das cidades, valor dos rendimentos pessoais, frequĂȘncia de ocorrĂȘncia de palavras em textos e magnitude de sismos, seguem distribuiçÔes do tipo Lei de PotĂȘncia. Estas distribuiçÔes indicam que pequenas ocorrĂȘncias sĂŁo muito comuns e grandes ocorrĂȘncias sĂŁo raras, podendo porĂ©m verificar-se com razoĂĄvel probabilidade. A finalidade deste trabalho visa a identificação de fenĂłmenos associados Ă s Leis de PotĂȘncia. Mostra-se o comportamento tĂpico destes fenĂłmenos, com os dados retirados dos vĂĄrios casos de estudo e com a ajuda de uma meta-anĂĄlise. As Leis de PotĂȘncia em sistemas naturais e artificiais apresentam uma proximidade a um padrĂŁo, quando os valores sĂŁo normalizados (frequĂȘncias relativas) para dar origem a um meta-grĂĄfico.
The Power Law is a feature of a nonlinear system, revealing a chaotic system near the self-organization. Some characteristics of natural and artificial systems, such as population size of cities, the value of personal income, the frequency of occurrence of words in texts and magnitude of earthquakes, follow a power law distribution. These distributions indicate that small occurrences are very common and large events are rare, but may occur with reasonable probability. The purpose of this work concerns the identification of phenomena associated with power laws. It is demonstrated a typical behavior of these phenomena, using data from several case studies and with the help of a meta-analysis. Power laws in natural and artificial systems have a proximity to a particular patterns, when values are normalized (relative frequencies) to give origin to a meta-graph.
The Power Law is a feature of a nonlinear system, revealing a chaotic system near the self-organization. Some characteristics of natural and artificial systems, such as population size of cities, the value of personal income, the frequency of occurrence of words in texts and magnitude of earthquakes, follow a power law distribution. These distributions indicate that small occurrences are very common and large events are rare, but may occur with reasonable probability. The purpose of this work concerns the identification of phenomena associated with power laws. It is demonstrated a typical behavior of these phenomena, using data from several case studies and with the help of a meta-analysis. Power laws in natural and artificial systems have a proximity to a particular patterns, when values are normalized (relative frequencies) to give origin to a meta-graph.
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Keywords
Lei de PotĂȘncia Lei de Zipf Lei de Pareto FenĂłmenos naturais FenĂłmenos artificiais Meta-grĂĄfico Meta-anĂĄlise Power Law Zipf Law Pareto Law Natural phenomena Artificial phenomena Meta-graph Meta-analysis
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Publisher
Instituto Politécnico do Porto. Instituto Superior de Engenharia do Porto