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      Practical Measures of Integrated Information for Time-Series Data

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      PLoS Computational Biology

      Public Library of Science

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          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          A recent measure of ‘integrated information’, Φ DM, quantifies the extent to which a system generates more information than the sum of its parts as it transitions between states, possibly reflecting levels of consciousness generated by neural systems. However, Φ DM is defined only for discrete Markov systems, which are unusual in biology; as a result, Φ DM can rarely be measured in practice. Here, we describe two new measures, Φ E and Φ AR, that overcome these limitations and are easy to apply to time-series data. We use simulations to demonstrate the in-practice applicability of our measures, and to explore their properties. Our results provide new opportunities for examining information integration in real and model systems and carry implications for relations between integrated information, consciousness, and other neurocognitive processes. However, our findings pose challenges for theories that ascribe physical meaning to the measured quantities.

          Author Summary

          A key feature of the human brain is its ability to represent a vast amount of information, and to integrate this information in order to produce specific and selective behaviour, as well as a stream of unified conscious scenes. Attempts have been made to quantify so-called ‘integrated information’ by formalizing in mathematics the extent to which a system as a whole generates more information than the sum of its parts. However, so far, the resulting measures have turned out to be inapplicable to real neural systems. In this paper we introduce two new measures that can be applied to both realistic neural models and to time-series data garnered from a broad range of neuroimaging and electrophysiological methods. Our work provides new opportunities for examining the role of integrated information in cognition and consciousness, and indeed in the function of any complex biological system. However, our results also pose challenges for theories that ascribe a direct physical meaning to any version of integrated information so far described.

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          Most cited references 23

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          Consciousness and complexity.

           G Edelman,  G Tononi (1998)
          Conventional approaches to understanding consciousness are generally concerned with the contribution of specific brain areas or groups of neurons. By contrast, it is considered here what kinds of neural processes can account for key properties of conscious experience. Applying measures of neural integration and complexity, together with an analysis of extensive neurological data, leads to a testable proposal-the dynamic core hypothesis-about the properties of the neural substrate of consciousness.
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            Consciousness as integrated information: a provisional manifesto.

             Giulio Tononi (2008)
            The integrated information theory (IIT) starts from phenomenology and makes use of thought experiments to claim that consciousness is integrated information. Specifically: (i) the quantity of consciousness corresponds to the amount of integrated information generated by a complex of elements; (ii) the quality of experience is specified by the set of informational relationships generated within that complex. Integrated information (Phi) is defined as the amount of information generated by a complex of elements, above and beyond the information generated by its parts. Qualia space (Q) is a space where each axis represents a possible state of the complex, each point is a probability distribution of its states, and arrows between points represent the informational relationships among its elements generated by causal mechanisms (connections). Together, the set of informational relationships within a complex constitute a shape in Q that completely and univocally specifies a particular experience. Several observations concerning the neural substrate of consciousness fall naturally into place within the IIT framework. Among them are the association of consciousness with certain neural systems rather than with others; the fact that neural processes underlying consciousness can influence or be influenced by neural processes that remain unconscious; the reduction of consciousness during dreamless sleep and generalized seizures; and the distinct role of different cortical architectures in affecting the quality of experience. Equating consciousness with integrated information carries several implications for our view of nature.
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              An information integration theory of consciousness

               Giulio Tononi (2004)
              Background Consciousness poses two main problems. The first is understanding the conditions that determine to what extent a system has conscious experience. For instance, why is our consciousness generated by certain parts of our brain, such as the thalamocortical system, and not by other parts, such as the cerebellum? And why are we conscious during wakefulness and much less so during dreamless sleep? The second problem is understanding the conditions that determine what kind of consciousness a system has. For example, why do specific parts of the brain contribute specific qualities to our conscious experience, such as vision and audition? Presentation of the hypothesis This paper presents a theory about what consciousness is and how it can be measured. According to the theory, consciousness corresponds to the capacity of a system to integrate information. This claim is motivated by two key phenomenological properties of consciousness: differentiation – the availability of a very large number of conscious experiences; and integration – the unity of each such experience. The theory states that the quantity of consciousness available to a system can be measured as the Φ value of a complex of elements. Φ is the amount of causally effective information that can be integrated across the informational weakest link of a subset of elements. A complex is a subset of elements with Φ>0 that is not part of a subset of higher Φ. The theory also claims that the quality of consciousness is determined by the informational relationships among the elements of a complex, which are specified by the values of effective information among them. Finally, each particular conscious experience is specified by the value, at any given time, of the variables mediating informational interactions among the elements of a complex. Testing the hypothesis The information integration theory accounts, in a principled manner, for several neurobiological observations concerning consciousness. As shown here, these include the association of consciousness with certain neural systems rather than with others; the fact that neural processes underlying consciousness can influence or be influenced by neural processes that remain unconscious; the reduction of consciousness during dreamless sleep and generalized seizures; and the time requirements on neural interactions that support consciousness. Implications of the hypothesis The theory entails that consciousness is a fundamental quantity, that it is graded, that it is present in infants and animals, and that it should be possible to build conscious artifacts.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS Comput Biol
                plos
                ploscomp
                PLoS Computational Biology
                Public Library of Science (San Francisco, USA )
                1553-734X
                1553-7358
                January 2011
                January 2011
                20 January 2011
                : 7
                : 1
                Affiliations
                Sackler Centre for Consciousness Science and School of Informatics, University of Sussex, Brighton, United Kingdom
                Indiana University, United States of America
                Author notes

                Conceived and designed the experiments: ABB AKS. Performed the experiments: ABB. Analyzed the data: ABB AKS. Contributed reagents/materials/analysis tools: ABB. Wrote the paper: ABB AKS.

                Article
                10-PLCB-RA-2391R3
                10.1371/journal.pcbi.1001052
                3024259
                21283779
                Barrett, Seth. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
                Page count
                Pages: 18
                Categories
                Research Article
                Neuroscience/Theoretical Neuroscience

                Quantitative & Systems biology

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