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Cited by 225Philosophy and Theoretical ScienceFunctional Brain Connectivity StudiesNeural dynamics and brain function

The DOI matches its Crossref record; 60 of the 61 references it cites were found in a registry or an index.

Practical Measures of Integrated Information for Time-Series Data

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Barrett, Adam B., Seth, Anil K.·2011·PLoS Computational Biology
DOI 10.1371/journal.pcbi.1001052PMC PMC3024259
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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.

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Crossref · 10.1371/journal.pcbi.1001052

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Figure 1 Integrated information in Markovian Gaussian systems. (a)–(g) Connectivity diagrams for seven systems as specified by the corresponding connectivity matrices . Arrow widths reflect connection strengths: for (a)–(c) and (e)–(g), all connection strengths are 0.25; for system (d) each connection strength is 1/14, thus the total afferent connection to each element is 0.5. (h) Integrated information, as measured by () for each of the systems (a)–(g), via simulated data (bars) and analytically via the generative model (asterisks). For simulated data, 10 trials were performed, with each trial generating 3000 data points. Bars show mean values; error bars show plus/minus one standard deviation. For system 1(g), sizes of sub-systems in the MIB varied across trials, falling into two distinct groups which are shown separately (the top bar reflects a group of 6 trials; the bottom bar, 4 trials).
Figure 1 Integrated information in Markovian Gaussian systems. (a)–(g) Connectivity diagrams for seven systems as specified by the corresponding connectivity matrices . Arrow widths reflect connection strengths: for (a)–(c) and (e)–(g), all connection strengths are 0.25; for system (d) each connection strength is 1/14, thus the total afferent connection to each element is 0.5. (h) Integrated information, as measured by () for each of the systems (a)–(g), via simulated data (bars) and analytically via the generative model (asterisks). For simulated data, 10 trials were performed, with each trial generating 3000 data points. Bars show mean values; error bars show plus/minus one standard deviation. For system 1(g), sizes of sub-systems in the MIB varied across trials, falling into two distinct groups which are shown separately (the top bar reflects a group of 6 trials; the bottom bar, 4 trials).CC BY · PubMed Central
Figure 2 Networks optimized for high integrated information. (a) Optimal network for 2 afferents of 0.25 to each node. This has . (b) Optimal network for total afferent of 0.5 to each node, and all connections to a given node equal. This has .
Figure 2 Networks optimized for high integrated information. (a) Optimal network for 2 afferents of 0.25 to each node. This has . (b) Optimal network for total afferent of 0.5 to each node, and all connections to a given node equal. This has .CC BY · PubMed Central
Figure 3 Examination of the landscape with respect to network connectivity. (a) Histogram of for the 30 networks in the final population of a GA that yielded optimal network 2(a). (b) Histogram of for the 30 networks in the final population of a GA that yielded optimal network 2(b). (c) Histogram of percentage decrease in following single mutations of network 2(a) (200 evaluations). (d) Histogram of percentage decrease in following single mutations of network 2(b) (200 evaluations). (e) Discontinuity in as connection strength from element 6 to element 1 continuously changes (network 2(a); (all other connections fixed at 0.25)).
Figure 3 Examination of the landscape with respect to network connectivity. (a) Histogram of for the 30 networks in the final population of a GA that yielded optimal network 2(a). (b) Histogram of for the 30 networks in the final population of a GA that yielded optimal network 2(b). (c) Histogram of percentage decrease in following single mutations of network 2(a) (200 evaluations). (d) Histogram of percentage decrease in following single mutations of network 2(b) (200 evaluations). (e) Discontinuity in as connection strength from element 6 to element 1 continuously changes (network 2(a); (all other connections fixed at 0.25)).CC BY · PubMed Central
Figure 4 Integrated information, measured for states multiple time-steps in the past, i.e. for varying . (a) Network 1(c). (b) Network 2(b). (c) Example MVAR(3) process, see Eq. (0.44).
Figure 4 Integrated information, measured for states multiple time-steps in the past, i.e. for varying . (a) Network 1(c). (b) Network 2(b). (c) Example MVAR(3) process, see Eq. (0.44).CC BY · PubMed Central
Figure 5 Stationary distributions for elements in networks animated with exponentially distributed noise. Each panel shows an empirical probability distribution as a histogram taken from 3000 data points from element 1 in (a) network 1(b), (b) network 1(d), and (c) network 2(b).
Figure 5 Stationary distributions for elements in networks animated with exponentially distributed noise. Each panel shows an empirical probability distribution as a histogram taken from 3000 data points from element 1 in (a) network 1(b), (b) network 1(d), and (c) network 2(b).CC BY · PubMed Central

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Metadata

Authors
Barrett, A. B., & Seth, A. K.
Affiliations
University of Sussex (GB)
Corresponding author
Barrett, Adam B.
ORCID
Venue
PLoS Computational Biology
Publisher
Public Library of Science (PLoS)
Published
2011-01-20
Volume
7
Issue
1
Pages
e1001052
ISSN
  • 1553-734X (ISSN-L)
  • 1553-7358
DOI
10.1371/journal.pcbi.1001052
PMC
PMC3024259
OpenAlex
W2048013965
Cited by
225
References
61
Citations by year
2026: 11 · 2025: 16 · 2024: 22 · 2023: 18 · 2022: 17 · 2021: 14 · 2020: 17 · 2019: 21 · 2018: 17 · 2017: 17 · 2016: 16 · 2015: 13 · 2014: 10 · 2013: 2 · 2012: 9
FWCI
10.30
Type
journal article
Language
en
Open access
Licence
Locations
  • PLoS Computational Biology (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • Sussex Research Online (University of Sussex) (submittedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • Figshare (submittedVersion, cc-by)
Funders
Engineering and Physical Sciences Research Council (EP/G007543/1)
Topics
  • Social Sciences › Arts and Humanities › Philosophy › Philosophy and Theoretical Science
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
Keywords
integrated information, information integration, time series, Markov systems, consciousness, neural systems, information measures
MeSH terms
Information Services, Markov Chains, Models, Theoretical

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