An Efficient Computational Model For The Minimum Information Partition Problem In The Context Of Integrated Information Theory (IIT)

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2025
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Universidad de Caldas
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Repositorio Institucional U. Caldas
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eng
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Palabra clave:
620 - Ingeniería y operaciones afines
2. Ingeniería y Tecnología
Integrated Information Theory (IIT)
Minimum Information Partition (MIP)
Submodularity
Optimization
Earth Mover’s Distance (EMD)
Queyranne’s algorithm
Consciousness Quantification,
Markovian systems.
Teoría de la Información Integrada
Partición de la Mínima Información
Submodularidad
Optimización
Distancia de Wasserstein (W1, EMD)
Algoritmo de Queyranne
Cuantificación de la Conciencia
Sistemas Markovianos
Ingeniería
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id REPOUCALDA_6ee1b9bf905ed163cfbabbc6c266ebfb
oai_identifier_str oai:repositorio.ucaldas.edu.co:ucaldas/22680
network_acronym_str REPOUCALDA
network_name_str Repositorio Institucional U. Caldas
repository_id_str
dc.title.none.fl_str_mv An Efficient Computational Model For The Minimum Information Partition Problem In The Context Of Integrated Information Theory (IIT)
Un modelo computacional eficiente para el problema de la partición de mínima información en el contexto de la teoría de la información integrada
title An Efficient Computational Model For The Minimum Information Partition Problem In The Context Of Integrated Information Theory (IIT)
spellingShingle An Efficient Computational Model For The Minimum Information Partition Problem In The Context Of Integrated Information Theory (IIT)
620 - Ingeniería y operaciones afines
2. Ingeniería y Tecnología
Integrated Information Theory (IIT)
Minimum Information Partition (MIP)
Submodularity
Optimization
Earth Mover’s Distance (EMD)
Queyranne’s algorithm
Consciousness Quantification,
Markovian systems.
Teoría de la Información Integrada
Partición de la Mínima Información
Submodularidad
Optimización
Distancia de Wasserstein (W1, EMD)
Algoritmo de Queyranne
Cuantificación de la Conciencia
Sistemas Markovianos
Ingeniería
title_short An Efficient Computational Model For The Minimum Information Partition Problem In The Context Of Integrated Information Theory (IIT)
title_full An Efficient Computational Model For The Minimum Information Partition Problem In The Context Of Integrated Information Theory (IIT)
title_fullStr An Efficient Computational Model For The Minimum Information Partition Problem In The Context Of Integrated Information Theory (IIT)
title_full_unstemmed An Efficient Computational Model For The Minimum Information Partition Problem In The Context Of Integrated Information Theory (IIT)
title_sort An Efficient Computational Model For The Minimum Information Partition Problem In The Context Of Integrated Information Theory (IIT)
dc.contributor.none.fl_str_mv Castillo Ossa, Luis Fernando
Inteligencia Artificial
de Miguel Casado, Gregorio
González Guerrero, Enrique
Gutiérrez Mosquera, Luís Fernando
dc.subject.none.fl_str_mv 620 - Ingeniería y operaciones afines
2. Ingeniería y Tecnología
Integrated Information Theory (IIT)
Minimum Information Partition (MIP)
Submodularity
Optimization
Earth Mover’s Distance (EMD)
Queyranne’s algorithm
Consciousness Quantification,
Markovian systems.
Teoría de la Información Integrada
Partición de la Mínima Información
Submodularidad
Optimización
Distancia de Wasserstein (W1, EMD)
Algoritmo de Queyranne
Cuantificación de la Conciencia
Sistemas Markovianos
Ingeniería
topic 620 - Ingeniería y operaciones afines
2. Ingeniería y Tecnología
Integrated Information Theory (IIT)
Minimum Information Partition (MIP)
Submodularity
Optimization
Earth Mover’s Distance (EMD)
Queyranne’s algorithm
Consciousness Quantification,
Markovian systems.
Teoría de la Información Integrada
Partición de la Mínima Información
Submodularidad
Optimización
Distancia de Wasserstein (W1, EMD)
Algoritmo de Queyranne
Cuantificación de la Conciencia
Sistemas Markovianos
Ingeniería
description Figuras
publishDate 2025
dc.date.none.fl_str_mv 2025-09-09T19:43:47Z
2025-09-09T19:43:47Z
2025
2030-10-30
dc.type.none.fl_str_mv Trabajo de grado - Doctorado
http://purl.org/coar/resource_type/c_db06
Text
info:eu-repo/semantics/doctoralThesis
dc.identifier.none.fl_str_mv https://repositorio.ucaldas.edu.co/handle/ucaldas/22680
Universidad de Caldas
Repositorio Institucional Universidad de Caldas
repositorio.ucaldas.edu.co
url https://repositorio.ucaldas.edu.co/handle/ucaldas/22680
identifier_str_mv Universidad de Caldas
Repositorio Institucional Universidad de Caldas
repositorio.ucaldas.edu.co
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Albantakis, L., Barbosa, L., Findlay, G., Grasso, M., Haun, A.M., Marshall, W., Mayner, W.G.P., Zaeemzadeh, A., Boly, M. (2023). Integrated information theory (IIT) 4.0: Formulating the properties of phenomenal existence in physical terms. PLoS Comput Biol, 19(10), e1011465.
Arsiwalla, X.D., Solé, R., Moulin-Frier, C., Herreros, I., Sánchez-Fibla, M. y Verschure, P.F.M.J. (2023). The morphospace of consciousness: three kinds of complexity for minds and machines. NeuroSci, 4(2), 79-102
Balduzzi, D. y Tononi, G. (2008). Integrated information in discrete dynamical systems: motivation and theoretical framework. PLOS Computational Biology, 4(6), e1000091.
Balduzzi, D. y Tononi, G. (2009). Qualia: the geometry of integrated information. PLoS Comput Biol, 5(8), e1000462.
Barbosa, L.S., Marshall, W., Streipert, S., Albantakis, L., Tononi, G. (2020). A measure for intrinsic information. Sci Rep, 10(1), 18803.
Barrett, A. y Seth, A.K. (2011). Practical measures of integrated information for time-series data. PLOS Computational Biology, 7(1), e1001052
Cacciotti, A., Pappalettera, C., Miraglia, F., Rossini, P.M. y Vecchio, F. (2024). EEG entropy insights in the context of physiological aging and Alzheimer's and Parkinson's diseases: a comprehensive review. Geroscience, 46(6), 5537-5557.
Coghlan, D. (2019). Doing action research in your Own Organization. fifth ed. Sage Publications
Coughlan, P. y Coghlan, D. (2002). Action research for operations management. International Journal of Operations & Production Management, 22(2), 220-240.
Fekete, T., Van Leeuwen, C. y Edelman, S. (2016). System, subsystem, hive: boundary problems in computational theories of consciousness. Frontiers in Psychology, 7(1041).
Gamez, D. (2020). The relationships between intelligence and consciousness in natural and artificial systems. Journal of Artificial Intelligence and Consciousness, 07(01), 51-62.
Gamez, D. y Holland, O. (2017). Artificial intelligence and consciousness.
Guerrero, L.E. (2023). Un modelo computacional eficiente para el problema de la partición de mínima información en el contexto de la teoría de la información integrada (IIT). Encuentro Internacional de Educación en Ingeniería.
Guerrero, L.E., Castillo, L.F., Arango-López, J. y Moreira, F. (2023). A systematic review of integrated information theory: a perspective from artificial intelligence and the cognitive sciences. Neural Computing and Applications.
Guerrero, L.E., Arango-López, J., Castillo, L.F., Correa, J.D. y Moreira, F. (2024a). Exploring alternatives to identify the partitioning of minimal information Loss.
Guerrero, L.E., Arango-López, J., Castillo, L.F. y Jaramillo-Garzón, J.A. (2024b). Efficient strategies for finding the minimum information partition in integrated information theory 3.0. Springer Nature Switzerland. Cham. 217-233.
Guerrero, L.E., Arango-López, J., Castillo, L.F. y Moreira, F. (2024c). Development of a model for the study and measurement of consciousness in artificial cognitive systems based on the integrated information theory. Neural Computing and Applications.
Guerrero, L.E., Arango-López, J., Castillo, L.F. y Moreira, F. (2024d). Integrated information theory with PyPhi: testing and improvement strategies. Information Systems and Technologies. Springer Nature Switzerland. Cham. 446-456.
Guerrero, L.E., Arango-López, J., Castillo, L.F. y Moreira, F. (2024e). Integrated information theory with PyPhi: testing and improvement strategies. Springer Nature Switzerland. Cham. 446-456.
Guerrero, L.E., Arango-López, J. y Castillo, L. (2025a). HDMP:A Heuristic-Driven memoization process for efficient minimum information partition in IIT.
Guerrero, L.E., Arango-López, J. y Castillo, L. (2025b). ACO-MIP: an ant colony optimization approach for minimum information partition in IIT.
Guerrero, L.E., Arango-López, J., Castillo, L. y Moreira, F. (2025c). A K-Means-Based strategy for estimating the MIP in integrated information theory.
Guerrero, L.E., Correa, J.D., Arango-López, J., Castillo, L. y Moreira, F. (2025d). QNodes: a scalable algorithm for efficient minimum information partition in integrated information theory.
Hidaka, S. y Oizumi, M. (2018). Fast and exact search for the partition with minimal information loss. PLOS ONE, 13(9), e0201126.
Hyvärinen, A. y Oja, E. (2000). Independent component analysis: algorithms and applications. Neural Networks, 13(4), 411-430.
Kim, M., Kim, H., Huang, Z., Mashour, G.A., Jordan, D., Ilg, R. y Lee, U. (2021). Criticality creates a functional platform for network transitions between internal and external processing modes in the human brain. Frontiers in Systems Neuroscience, 15.
Kitazono, J. y Oizumi M. (2018). Practical PHI Toolbox
Kitazono, J., Kanai, R. y Oizumi, M. (2018). Efficient algorithms for searching the minimum information partition in integrated information theory. Entropy, (20), 173.
Koch, C. (2009). A theory of consciousness. Scientific American Mind, (20), 16-19.
Kriegeskorte, N. y Douglas, P.K. (2018). Cognitive computational neuroscience. Nature Neuroscience, 21(9), 1148-1160.
Krohn, S. y Ostwald, D. (2017). Computing integrated information. Neuroscience of Consciousness, (1).
Luppi, A.I., Mediano, P.A.M., Rosas, F.E., Allanson, J., Pickard, J., Carhart-Harris, R.L., Williams, G.B., Craig, M.M. y Finoia, P. (2024). A synergistic workspace for human consciousness revealed by integrated information decomposition. eLife, (12), RP88173
Marshall, W., Grasso, M., Mayner, W.G.P., Zaeemzadeh, A., Barbosa, L.S., Chastain, E., Findlay, G., Sasai, S., Albantakis, L. y Tononi, G. (2023). System Integrated Information. Entropy, 25(2), 334.
Mayner, W.G.P., Marshall, W., Albantakis, L., Findlay, G., Marchman, R. y Tononi, G. (2018). PyPhi: a toolbox for integrated information theory. PLOS Computational Biology, 14(7), e1006343.
Mediano, P.A.M., Rosas F., Carhart-Harris, R., Seth, A. y Barrett, A. (2019). Beyond integrated information: a taxonomy of information dynamics phenomena. arXiv: Neurons and Cognition
Nemirovsky, I.E., Popiel, N.J.M., Rudas, J., Caius, M., Naci, L., Schiff, N.D., Owen, A.M. y Soddu, A. (2023). An implementation of integrated information theory in resting-state fMRI. Communications Biology, 6(1), 692.
Nilsen, A.S., Juel, B. y Marshall, W. (2019). Evaluating approximations and heuristic measures of integrated information. Entropy, (21), 525.
Oizumi, M., Albantakis, L. y Tononi, G. (2014). From the phenomenology to the mechanisms of consciousness: integrated information theory 3.0. PLOS Computational Biology, 10(5).
Olesen, C., Waade, P.T., Albantakis, L. y Mathys, C. (2023). Phi fluctuates with surprisal: an empirical pre-study for the synthesis of the free energy principle and integrated information theory. PLOS Computational Biology, 19(10), e1011346.
Patnaik, L.M. y Kallimani, J.S. (2017). Promises and limitations of conscious machines. In: Menon, S., Nagaraj, N., Binoy, V.V. (Eds.). Self, culture and consciousness: interdisciplinary convergences on knowing and being. Springer Singapore: Singapore. 79-92.
Pele, O. y Werman, M. (2009). Fast and robust earth mover's distances. 2009 IEEE 12th International Conference on Computer Vision. 460-467.
Tanco, J.A. y Camarero, L.A. (2013). Investigación en acción: cómo impulsar la contribución de la universidad en la competitividad de las organizaciones
Tegmark, M. (2016). Improved measures of integrated information. PLOS Computational Biology, 12(11), e1005123.
Toker, D. y Sommer, F.T. (2019). Information integration in large brain networks. PLOS Computational Biology, 15(2), e1006807.
Tononi, G. (2004). An information integration theory of consciousness. BMC Neuroscience, 5(1), 42.
Tononi, G. (2008). Consciousness as integrated information: a provisional manifesto. Biol Bull, 215(3), 216-242.
Tononi, G. y Koch, C. (2015). Consciousness: here, there and everywhere? Philosophical transactions of the Royal Society of London. Series B, Biological sciences, (370).
Tononi, G., Boly, M., Massimini, M. y Koch, C. (2016). Integrated information theory: from consciousness to its physical substrate. Nature Reviews Neuroscience, 17(7), 450-461
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dc.format.none.fl_str_mv 152 páginas
application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Universidad de Caldas
Facultad de Inteligencia Artificial e Ingenierías
Colombia, Caldas, Manizales
Doctorado en Ingeniería
publisher.none.fl_str_mv Universidad de Caldas
Facultad de Inteligencia Artificial e Ingenierías
Colombia, Caldas, Manizales
Doctorado en Ingeniería
institution Universidad de Caldas
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1855532631528046592
spelling An Efficient Computational Model For The Minimum Information Partition Problem In The Context Of Integrated Information Theory (IIT)Un modelo computacional eficiente para el problema de la partición de mínima información en el contexto de la teoría de la información integrada620 - Ingeniería y operaciones afines2. Ingeniería y TecnologíaIntegrated Information Theory (IIT)Minimum Information Partition (MIP)SubmodularityOptimizationEarth Mover’s Distance (EMD)Queyranne’s algorithmConsciousness Quantification,Markovian systems.Teoría de la Información IntegradaPartición de la Mínima InformaciónSubmodularidadOptimizaciónDistancia de Wasserstein (W1, EMD)Algoritmo de QueyranneCuantificación de la ConcienciaSistemas MarkovianosIngenieríaFigurasEsta tesis doctoral aborda uno de los principales desafíos computacionales de la Teoría de la Información Integrada (IIT): la determinación eficiente de la Partición de Mínima Información (MIP). La IIT, propuesta por Giulio Tononi, ofrece un marco matemático para cuantificar la consciencia mediante la medida Phi (Φ), que representa el nivel de información integrada en un sistema. Sin embargo, calcular Φ requiere identificar la MIP, un problema computacionalmente intratable debido al crecimiento exponencial de particiones posibles (2^(N-1)-1 para N elementos). La investigación introduce QNodes, una estrategia computacional innovadora que transforma este problema de complejidad exponencial O(2^N) en uno de complejidad polinomial O(N³). Esta transformación se logra mediante: (1) la demostración formal de la submodularidad de la función de pérdida basada en la Distancia de Wasserstein (EMD), (2) la aplicación del algoritmo de Queyranne para optimización submodular, y (3) el desarrollo de una representación multidimensional eficiente usando N-cubos para manipular distribuciones de probabilidad condicionales. Los resultados experimentales demuestran que QNodes mantiene una precisión del 100% en la identificación del MIP comparado con métodos exhaustivos, mientras logra mejoras exponenciales en tiempo de ejecución y uso de memoria. La estrategia permite analizar exitosamente sistemas de hasta 22 elementos, extendiendo significativamente el alcance práctico de la IIT más allá de los límites previos de aproximadamente 6-10 elementos. Las contribuciones principales incluyen: la prueba matemática de submodularidad, la arquitectura N-cubo para operaciones probabilísticas eficientes, y la validación empírica con datos sintéticos y neurofisiológicos reales. Este trabajo transforma la IIT de un marco principalmente teórico a una herramienta computacionalmente viable para el estudio de la consciencia en sistemas complejos, con aplicaciones potenciales en neurociencia, inteligencia artificial y ciencias cognitivas.This doctoral thesis addresses one of the main computational challenges of Integrated Information Theory (IIT): the efficient determination of the Minimum Information Partition (MIP). IIT, proposed by Giulio Tononi, offers a mathematical framework to quantify consciousness through the measure Phi (Φ), which represents the level of integrated information in a system. However, calculating Φ requires identifying the MIP, a computationally intractable problem due to the exponential growth of possible partitions (2^(N-1)-1 for N elements). The research introduces QNodes, an innovative computational strategy that transforms this exponential complexity problem O(2^N) into polynomial complexity O(N³). This transformation is achieved through: (1) formal demonstration of the submodularity of the Earth Mover's Distance (EMD)-based loss function, (2) application of Queyranne's algorithm for submodular optimization, and (3) development of an efficient multidimensional representation using N-cubes to manipulate conditional probability distributions. Experimental results demonstrate that QNodes maintains 100% accuracy in MIP identification compared to exhaustive methods, while achieving exponential improvements in execution time and memory usage. The strategy successfully analyzes systems with up to 22 elements, significantly extending the practical scope of IIT beyond previous limits of approximately 6-10 elements. Main contributions include: mathematical proof of submodularity, N-cube architecture for efficient probabilistic operations, and empirical validation with synthetic and real neurophysiological data. This work transforms IIT from a primarily theoretical framework to a computationally viable tool for studying consciousness in complex systems, with potential applications in neuroscience, artificial intelligence, and cognitive sciences.Chapter 1. Introduction -- Background -- Justification -- Hypothesis -- Objectives -- General objective -- Specific objectives -- Research methodology -- Characteristics of the AR approach -- Phases of the AR approach -- Applications and expected results -- Structure of the document -- Chapter 2. Theoretical framework -- Artificial intelligence, cognitive systems, and IIT: an exploratory framework -- Algorithmic approaches -- Methodological frameworks -- Modeling techniques -- Software applications -- Integrated information theory -- The minimum information partition (MIP) problem -- PyPhi and other computational tools -- Mathematical foundations: EMD and submodularity -- Earth mover's distance -- Submodularity -- Optimization algorithms and computational approaches -- Queyranne's algorithm -- Metaheuristics and approximation algorithms -- Machine learning and clustering approaches -- Dynamic programming and memoization -- Top-down recursive decomposition -- Memoization implementation -- Chapter 3. Methodological framework -- Evolutionary trajectory of research -- Initial exploratory phase -- Preliminary approaches development phase -- Consolidation and optimization phase -- Methodological contributions of developed work -- Role of publications in the research framework -- Research development stages -- Consolidation in the QNodes strategy -- Chapter 4. A systematic review of integrated information theory: a perspective from artificial intelligence and the cognitive sciences -- Publication information -- Original publication -- Chapter 5. Development of a model for the study and measurement of consciousness in artificial cognitive systems based on the integrated information theory -- Publication information -- Original publication -- Chapter 6. QNodes: A scalable algorithm for efficient minimum information partitioning in integrated information theory -- Publication information -- Original publication -- Chapter 7. Evidence and results -- Achievement of objectives -- Published articles -- Articles under review -- Projects -- Chapter 8. Conclusions -- Fundamental methodological findings -- Innovations in representation and algorithms -- Theoretical and practical implications -- Implications for integrated information theory -- Relevance and applications in various domains -- Limitations and future directions -- Main contributions -- Chapter 9. Bibliographic references.DoctoradoDoctor(a) en IngenieríaSistemas Cognitivos ArtificialesUniversidad de CaldasFacultad de Inteligencia Artificial e IngenieríasColombia, Caldas, ManizalesDoctorado en IngenieríaCastillo Ossa, Luis FernandoInteligencia Artificialde Miguel Casado, GregorioGonzález Guerrero, EnriqueGutiérrez Mosquera, Luís FernandoGuerrero Mendieta, Luz Enith2025-09-09T19:43:47Z2030-10-302025-09-09T19:43:47Z2025Trabajo de grado - Doctoradohttp://purl.org/coar/resource_type/c_db06Textinfo:eu-repo/semantics/doctoralThesis152 páginasapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttps://repositorio.ucaldas.edu.co/handle/ucaldas/22680Universidad de CaldasRepositorio Institucional Universidad de Caldasrepositorio.ucaldas.edu.coengAlbantakis, L., Barbosa, L., Findlay, G., Grasso, M., Haun, A.M., Marshall, W., Mayner, W.G.P., Zaeemzadeh, A., Boly, M. (2023). Integrated information theory (IIT) 4.0: Formulating the properties of phenomenal existence in physical terms. PLoS Comput Biol, 19(10), e1011465.Arsiwalla, X.D., Solé, R., Moulin-Frier, C., Herreros, I., Sánchez-Fibla, M. y Verschure, P.F.M.J. (2023). The morphospace of consciousness: three kinds of complexity for minds and machines. NeuroSci, 4(2), 79-102Balduzzi, D. y Tononi, G. (2008). Integrated information in discrete dynamical systems: motivation and theoretical framework. PLOS Computational Biology, 4(6), e1000091.Balduzzi, D. y Tononi, G. (2009). Qualia: the geometry of integrated information. PLoS Comput Biol, 5(8), e1000462.Barbosa, L.S., Marshall, W., Streipert, S., Albantakis, L., Tononi, G. (2020). A measure for intrinsic information. Sci Rep, 10(1), 18803.Barrett, A. y Seth, A.K. (2011). Practical measures of integrated information for time-series data. PLOS Computational Biology, 7(1), e1001052Cacciotti, A., Pappalettera, C., Miraglia, F., Rossini, P.M. y Vecchio, F. (2024). EEG entropy insights in the context of physiological aging and Alzheimer's and Parkinson's diseases: a comprehensive review. Geroscience, 46(6), 5537-5557.Coghlan, D. (2019). Doing action research in your Own Organization. fifth ed. Sage PublicationsCoughlan, P. y Coghlan, D. (2002). Action research for operations management. International Journal of Operations & Production Management, 22(2), 220-240.Fekete, T., Van Leeuwen, C. y Edelman, S. (2016). System, subsystem, hive: boundary problems in computational theories of consciousness. Frontiers in Psychology, 7(1041).Gamez, D. (2020). The relationships between intelligence and consciousness in natural and artificial systems. Journal of Artificial Intelligence and Consciousness, 07(01), 51-62.Gamez, D. y Holland, O. (2017). Artificial intelligence and consciousness.Guerrero, L.E. (2023). Un modelo computacional eficiente para el problema de la partición de mínima información en el contexto de la teoría de la información integrada (IIT). Encuentro Internacional de Educación en Ingeniería.Guerrero, L.E., Castillo, L.F., Arango-López, J. y Moreira, F. (2023). A systematic review of integrated information theory: a perspective from artificial intelligence and the cognitive sciences. Neural Computing and Applications.Guerrero, L.E., Arango-López, J., Castillo, L.F., Correa, J.D. y Moreira, F. (2024a). Exploring alternatives to identify the partitioning of minimal information Loss.Guerrero, L.E., Arango-López, J., Castillo, L.F. y Jaramillo-Garzón, J.A. (2024b). Efficient strategies for finding the minimum information partition in integrated information theory 3.0. Springer Nature Switzerland. Cham. 217-233.Guerrero, L.E., Arango-López, J., Castillo, L.F. y Moreira, F. (2024c). Development of a model for the study and measurement of consciousness in artificial cognitive systems based on the integrated information theory. Neural Computing and Applications.Guerrero, L.E., Arango-López, J., Castillo, L.F. y Moreira, F. (2024d). Integrated information theory with PyPhi: testing and improvement strategies. Information Systems and Technologies. Springer Nature Switzerland. Cham. 446-456.Guerrero, L.E., Arango-López, J., Castillo, L.F. y Moreira, F. (2024e). Integrated information theory with PyPhi: testing and improvement strategies. Springer Nature Switzerland. Cham. 446-456.Guerrero, L.E., Arango-López, J. y Castillo, L. (2025a). HDMP:A Heuristic-Driven memoization process for efficient minimum information partition in IIT.Guerrero, L.E., Arango-López, J. y Castillo, L. (2025b). ACO-MIP: an ant colony optimization approach for minimum information partition in IIT.Guerrero, L.E., Arango-López, J., Castillo, L. y Moreira, F. (2025c). A K-Means-Based strategy for estimating the MIP in integrated information theory.Guerrero, L.E., Correa, J.D., Arango-López, J., Castillo, L. y Moreira, F. (2025d). QNodes: a scalable algorithm for efficient minimum information partition in integrated information theory.Hidaka, S. y Oizumi, M. (2018). Fast and exact search for the partition with minimal information loss. PLOS ONE, 13(9), e0201126.Hyvärinen, A. y Oja, E. (2000). Independent component analysis: algorithms and applications. Neural Networks, 13(4), 411-430.Kim, M., Kim, H., Huang, Z., Mashour, G.A., Jordan, D., Ilg, R. y Lee, U. (2021). Criticality creates a functional platform for network transitions between internal and external processing modes in the human brain. Frontiers in Systems Neuroscience, 15.Kitazono, J. y Oizumi M. (2018). Practical PHI ToolboxKitazono, J., Kanai, R. y Oizumi, M. (2018). Efficient algorithms for searching the minimum information partition in integrated information theory. Entropy, (20), 173.Koch, C. (2009). A theory of consciousness. Scientific American Mind, (20), 16-19.Kriegeskorte, N. y Douglas, P.K. (2018). Cognitive computational neuroscience. Nature Neuroscience, 21(9), 1148-1160.Krohn, S. y Ostwald, D. (2017). Computing integrated information. Neuroscience of Consciousness, (1).Luppi, A.I., Mediano, P.A.M., Rosas, F.E., Allanson, J., Pickard, J., Carhart-Harris, R.L., Williams, G.B., Craig, M.M. y Finoia, P. (2024). A synergistic workspace for human consciousness revealed by integrated information decomposition. eLife, (12), RP88173Marshall, W., Grasso, M., Mayner, W.G.P., Zaeemzadeh, A., Barbosa, L.S., Chastain, E., Findlay, G., Sasai, S., Albantakis, L. y Tononi, G. (2023). System Integrated Information. Entropy, 25(2), 334.Mayner, W.G.P., Marshall, W., Albantakis, L., Findlay, G., Marchman, R. y Tononi, G. (2018). PyPhi: a toolbox for integrated information theory. 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