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      Shannon entropy of brain functional complex networks under the influence of the psychedelic Ayahuasca

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          Abstract

          The entropic brain hypothesis holds that the key facts concerning psychedelics are partially explained in terms of increased entropy of the brain’s functional connectivity. Ayahuasca is a psychedelic beverage of Amazonian indigenous origin with legal status in Brazil in religious and scientific settings. In this context, we use tools and concepts from the theory of complex networks to analyze resting state fMRI data of the brains of human subjects under two distinct conditions: (i) under ordinary waking state and (ii) in an altered state of consciousness induced by ingestion of Ayahuasca. We report an increase in the Shannon entropy of the degree distribution of the networks subsequent to Ayahuasca ingestion. We also find increased local and decreased global network integration. Our results are broadly consistent with the entropic brain hypothesis. Finally, we discuss our findings in the context of descriptions of “mind-expansion” frequently seen in self-reports of users of psychedelic drugs.

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          Most cited references 44

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          Statistical mechanics of complex networks

          Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.
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            Neural networks and physical systems with emergent collective computational abilities.

             John Hopfield (1982)
            Computational properties of use of biological organisms or to the construction of computers can emerge as collective properties of systems having a large number of simple equivalent components (or neurons). The physical meaning of content-addressable memory is described by an appropriate phase space flow of the state of a system. A model of such a system is given, based on aspects of neurobiology but readily adapted to integrated circuits. The collective properties of this model produce a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size. The algorithm for the time evolution of the state of the system is based on asynchronous parallel processing. Additional emergent collective properties include some capacity for generalization, familiarity recognition, categorization, error correction, and time sequence retention. The collective properties are only weakly sensitive to details of the modeling or the failure of individual devices.
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              Finding and evaluating community structure in networks

               M. Newman,  M Girvan (2003)
              We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.
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                Author and article information

                Contributors
                aline.viol@ufv.br
                Journal
                Sci Rep
                Sci Rep
                Scientific Reports
                Nature Publishing Group UK (London )
                2045-2322
                7 August 2017
                7 August 2017
                2017
                : 7
                Affiliations
                [1 ]ISNI 0000 0000 9687 399X, GRID grid.411233.6, Department of Physics, , Universidade Federal do Rio Grande do Norte, ; 59078-970 Natal, RN Brazil
                [2 ]ISNI 0000 0004 0400 2468, GRID grid.410484.d, Computational Biology Center, , T. J. Watson Research Center, IBM, ; 10598 Yorktown Heights, NY USA
                [3 ]ISNI 0000 0000 8338 6359, GRID grid.12799.34, Department of Physics, , Universidade Federal de Viçosa, ; 36570-000 Viçosa, MG Brazil
                [4 ]ISNI 0000 0000 9687 399X, GRID grid.411233.6, Brain Institute, , Universidade Federal do Rio Grande do Norte, ; 59078-970 Natal, RN Brazil
                [5 ]ISNI 0000 0000 9687 399X, GRID grid.411233.6, , National Institute of Science and Technology of Complex Systems Universidade Federal do Rio Grande do Norte, ; 59078-970 Natal, RN Brazil
                Article
                6854
                10.1038/s41598-017-06854-0
                5547073
                © The Author(s) 2017

                Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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