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Decomposition of inflationary systems into scale-free networks
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Resumo(s)
Due to their overly complex nature, real-world networks cannot be understood through typical mathematic tools, such as diferential equations, for that reason we use networks and analyse them through algorithms to understand them. This work focuses on decomposing scale-free networks into Barabási-Albert networks to better understand them. We are able to make an analysis of these networks through their decomposition and to identify redundant data to reduce size and complexity. We use tools such as autoencoders to create the algorithms and to go from integer-dimensional spaces to networks and vice versa. An integer dimension space, such as a Euclidian space is a projection of a network, for the case of BA (Barabási-Albert) networks, in the limit they tend to a one-dimension space, or a curved line. We can make use of this notion to try and recreate the original integer dimension space from the created BA networks. We can tested these concepts using a network whose projection is a Euclidian space and a market network, whose projection is a fractal space, which are created with the help of autoencoders. Autoencoders are also used to try and understand their differences and to validate the results. An accuracy analysis will be made in order to identify redundant data in the networks and possibly simplify them. This work can help to simplify and better comprehend real-world networks, such as the stock market and social networks.
Descrição
Tese de Mestrado, Engenharia Física, 2025, Universidade de Lisboa, Faculdade de Ciências
Palavras-chave
Barabási-Albert autoencoders integer-dimensional spaces scale-free networks