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On the complexity of boolean networks

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dc.contributor.advisor Ugalde Saldaña, Edgardo
dc.contributor.author Zúñiga Pérez, Edgar Alberto
dc.contributor.illustrator CVU 19272 ORCID 0000-0003-4450-932X es_MX
dc.coverage.temporal México. San Luis Potosí. San Luis Potosí es_MX
dc.date.accessioned 2020-07-25T00:21:05Z
dc.date.available 2020-07-25T00:21:05Z
dc.date.issued 2019-08
dc.identifier.uri https://repositorioinstitucional.uaslp.mx/xmlui/handle/i/5819
dc.description.abstract The Boolean Networks are a model which has proven to be useful to model realworld systems. The Random Boolean Network model introduced by Kau man in 1969 has been extensively used to model regulatory genetic networks and other types of systems. In this thesis, we propose the existence of a correlation between the complexity of a Boolean Network and the complexity of its constituents, i.e., the complexity of its topology and its set of updating functions. This hypothesis was tested by performing a series of experiments with the help of the implementation to approximate Kolmogorov complexity called Block Decomposition Method (BDM). First, we present a method to measure the complexity of the individual components of a Boolean Network and then, we propose a representation which can be used to measure the complexity of a Boolean Network. The results showed that this hypothesis was correct for Random Boolean Networks with small topologies given a su ciently large set of Boolean Networks. However, it could not be generalized to larger topologies because of the enormous computational time required by the implementation of the BDM to approximate Kolmogorov complexity. Finally, the di culties to measure the complexities of Random Boolean Networks with larger topologies inspired us to propose a novel method to measure Kolmogorov complexity. We have called this method the Block Decomposition Method with Neural Networks (BDMNN) and is based on the use of Neural Networks to perform a regression that approximates Kolmogorov complexity. These Neural Networks were trained by using random sequences for which its complexity was computed using the original BDM implementation to approximate Kolmogorov complexity. Our implementation was evaluated by performing some experiments with random sequences of bits. The results showed that our implementation is faster and requires less computational power to approximate Kolmogorov complexity than the original implementation. The only cost to be paid is a decrease in the accuracy of the results, however, we expect this error can be easily reduced with some little modi cations to the method. es_MX
dc.description.statementofresponsibility Investigadores es_MX
dc.description.statementofresponsibility Estudiantes es_MX
dc.language Inglés es_MX
dc.relation.ispartofseries Maestría en Ciencias Física. Facultad de Ciencias. Universidad Autónoma de San Luis Potosí es_MX
dc.relation.haspart Consejo Nacional de Ciencia y Tecnología es_MX
dc.rights Acceso Abierto es_MX
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0 es_MX
dc.subject.classification CIENCIAS FÍSICO MATEMATICAS Y CIENCIAS DE LA TIERRA es_MX
dc.title On the complexity of boolean networks es_MX
dc.type Tesis de maestría es_MX


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