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The integrated information Φ of an integrate and fire network.

Code ↔ Paper

1 match between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

The 1 match
  1. [1] § Methods › PyPhi module ↔ 2_matrix_reader.py, lines 7–21 · score 0.53 · Transition Probability Matrix, Connectivity Matrix, CM, PyPhi, TPM, nodes

Paper

Loaded from Europe PMC by your browser, not stored by OSCR: doi.org · Europe PMC

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The authors' code

Python · 77 lines · 2.4 KB · no license · 1 match

  1. # ipython3
  2. import pyphi
  3. import numpy as np
  4. import itertools as it
  5. # http://integratedinformationtheory.org/calculate.html
  7. print()
  8. print('UNCUT VERSION')
  9. # transition probability matrix
  10. # multi-dim state-by-node form
  11. tpm = np.load("files_matrices/tpm1.npy", fix_imports=True)
  12. tpm_sbs = pyphi.convert.state_by_node2state_by_state(tpm)
  13. print()
  14. print('Transition Probability Matrix (state-by-state form):')
  15. print(tpm_sbs)
  16. print()
  17. cm = np.load("files_matrices/cm1.npy", fix_imports=True)
  18. print('Connectivity Matrix:')
  19. print(cm)
  20. print()
  21. netsize = np.shape(cm)[0]
  23. # network nodes labels, numeration, network states list
  24. node_indices = tuple(range(netsize))
  25. start_states = list(it.product([0, 1], repeat = netsize))
  26. unreachable_states = list()
  27. # create network
  28. network = pyphi.Network(tpm, cm=cm)
  30. # subsystem consists of network[selected nodes] + state
  31. # calculate phi
  32. for state in start_states:
  33. try:
  34. subsystem = pyphi.Subsystem(network, state, node_indices)
  35. pyphi_value = pyphi.compute.phi(subsystem)
  36. if(pyphi_value): print('state', state, ': pyphi value (uncut)= ', pyphi_value)
  37. except ValueError:
  38. unreachable_states.append(state)
  39. pass
  40. # print unreachable states info parameter
  41. for u_state in unreachable_states:
  42. print('state', u_state, ': unreachable (uncut)')
  43. print()
  45. print()
  46. print('CUT VERSION')
  47. tpm_cut = np.load("files_matrices/tpm1_cut.npy", fix_imports=True)
  48. tpm_sbs_cut = pyphi.convert.state_by_node2state_by_state(tpm_cut)
  49. print('Cut Transition Probability Matrix (state-by-state form):')
  50. print(tpm_sbs_cut)
  51. cm_cut = np.load("files_matrices/cm1_cut.npy", fix_imports=True)
  52. print('Cut Connectivity Matrix:')
  53. print(cm_cut)
  54. print()
  55. netsize = np.shape(cm_cut)[0]
  57. # network nodes labels, numeration, network states list
  58. node_indices = tuple(range(netsize))
  59. start_states = list(it.product([0, 1], repeat = netsize))
  60. unreachable_states = list()
  61. # create network
  62. network = pyphi.Network(tpm_cut, cm=cm_cut)
  64. # subsystem consists of network[selected nodes] + state
  65. # calculate phi
  66. for state in start_states:
  67. try:
  68. subsystem = pyphi.Subsystem(network, state, node_indices)
  69. pyphi_value = pyphi.compute.phi(subsystem)
  70. if(pyphi_value): print('state', state, ': pyphi value (cut)= ', pyphi_value)
  71. except ValueError:
  72. unreachable_states.append(state)
  73. pass
  74. # print unreachable states info parameter
  75. for u_state in unreachable_states:
  76. print('state', u_state, ': unreachable (cut)')
  77. print()

2_matrix_reader.py at commit b572950, no license · at the source

Overview

Authors: Miłosz Danilczuk1, Marek Pokropski2, Piotr Suffczynski1
ORCID iDs: Marek Pokropski, Piotr Suffczynski
  1. Faculty of Physics, University of Warsaw, Warsaw, Poland
  2. Faculty of Philosophy, University of Warsaw, Warsaw, Poland
Institutions: University of Warsaw (Poland)
Journal: PLoS computational biology, volume 22, issue 3, article e1014085
Dates: received 16 April 2025; accepted 3 March 2026; published online 9 March 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1371/journal.pcbi.1014085 · PMID 41801929 · PMCID PMC12991358 · OpenAlex W7134253203
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: computational modeling (no new data) (modality), human (organism), computational (subfield)
MeSH: Action Potentials*, Information Theory*, Models, Neurological*, Nerve Net*, Neurons*, Animals, Computational Biology, Computer Simulation, Consciousness, Humans (* major topic)
Journal subjects: Biology and Life Sciences, Cell Biology, Cellular Types, Animal Cells, Neurons, Neuroscience, Cellular Neuroscience, Computer and Information Sciences, Neural Networks, Physiology, Electrophysiology, Membrane Potential, Action Potentials, Neurophysiology, Engineering and Technology, Electronics Engineering, Logic Circuits, Cognitive Science, Cognitive Neuroscience, Consciousness, Systems Science, Dynamical Systems, Physical Sciences, Mathematics, Theories of Consciousness
Topic: Neural dynamics and brain function (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Citations: not cited yet (Europe PMC); 37 references in the paper

Abstract

Integrated Information Theory is a theoretical framework proposing that consciousness is a fundamental property of systems capable of integrating information. To bridge the gap between the theoretical concept and the practical use in actual neurobiological systems, we have applied the Integrated Information Theory approach to a simulated network of integrate and fire neurons (IAF). The primary contribution of this study is several empirical findings. Our analysis shows that such a network can possess a non-zero Φ value under certain conditions and parameter settings. Additionally, our research indicates that the complexity of the network’s dynamics doesn’t necessarily correlate with its Φ value. On the other hand, the quantity of integrated information within the network appears to grow with the IAF neurons’ time constant, which reflects their integrative capacity. Furthermore, our examination of the integrate and fire network with internal random fluctuations demonstrates that the integrated information measure, as defined in IIT version 3.0, is not resilient to noise.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above, with 1 match between paragraphs and lines of code.

mdanilczuk/IITfire

License: none: the authors keep all their rights
State: the link answers, verified on 30 September 2026
Evidence: files inventoried
Commit: b572950082e52d0a94bd4e345908437bb305f553, 17 April 2025
Languages: Python (6), Shell (1)
Size: 8 files, 7 scripts
Software Heritage: not checked
Found in: “Data Availability”
Holds: README
Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: NumPy (6 files), Matplotlib (5 files)
Availability: 1 check, the latest on 30 September 2026: the link answers
  • 30 September 2026: the link answers
8 files
At the source: github.com/mdanilczuk/IITfire

The paper's code and data availability statement is in the Data section.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 7 scripts, each with its path and the digest of its content;
  • 1 match between paragraphs of the paper and lines of the code (method lexical-v1);
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

No dataset and no data link were found in the paper.

Data Availability

The software used in the manuscript is publicly available in the PyPhi Python library created by the IIT developers. A custom script for TPM calculation is freely available at: https://github.com/mdanilczuk/IITfire.

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.

Version 1, 30 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 10 MeSH terms, 32 references.

Cite

This paper

Danilczuk, M., Pokropski, M., & Suffczynski, P. (2026). The integrated information Φ of an integrate and fire network. PLoS computational biology, 22(3), e1014085. https://doi.org/10.1371/journal.pcbi.1014085

BibTeX

@article{danilczuk2026integrated,
author = {Danilczuk, Miłosz and Pokropski, Marek and Suffczynski, Piotr},
title = {{The integrated information Φ of an integrate and fire network}},
journal = {PLoS computational biology},
year = {2026},
month = mar,
volume = {22},
number = {3},
pages = {e1014085},
publisher = {PLOS},
issn = {1553-734X},
doi = {10.1371/journal.pcbi.1014085},
url = {https://doi.org/10.1371/journal.pcbi.1014085},
pmid = {41801929},
pmcid = {PMC12991358}
}

RIS

TY - JOUR
AU - Danilczuk, Miłosz
AU - Pokropski, Marek
AU - Suffczynski, Piotr
TI - The integrated information Φ of an integrate and fire network
T2 - PLoS computational biology
J2 - PLoS Comput Biol
PY - 2026
DA - 2026/03/09
VL - 22
IS - 3
SP - e1014085
SN - 1553-734X
PB - PLOS
DO - 10.1371/journal.pcbi.1014085
UR - https://doi.org/10.1371/journal.pcbi.1014085
LA - en
ER -

CSL-JSON

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"id": "10.1371/journal.pcbi.1014085",
"type": "article-journal",
"title": "The integrated information Φ of an integrate and fire network",
"container-title": "PLoS computational biology",
"author": [
{
"family": "Danilczuk",
"given": "Miłosz"
},
{
"family": "Pokropski",
"given": "Marek"
},
{
"family": "Suffczynski",
"given": "Piotr"
}
],
"container-title-short": "PLoS Comput Biol",
"volume": "22",
"issue": "3",
"page": "e1014085",
"DOI": "10.1371/journal.pcbi.1014085",
"PMID": "41801929",
"PMCID": "PMC12991358",
"ISSN": "1553-734X",
"publisher": "PLOS",
"URL": "https://doi.org/10.1371/journal.pcbi.1014085",
"language": "en",
"issued": {
"date-parts": [
[
2026,
3,
9
]
]
}
}

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