---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '19796'
abstract:
- lang: eng
  text: "Motivation: Boolean networks are popular dynamical models of cellular processes
    in systems biology. Their attractors model phenotypes that arise from the interplay
    of key regulatory subcircuits. A succession diagram (SD) describes this interplay
    in a discrete analog of Waddington’s epigenetic attractor landscape that allows
    for fast identification of attractors and attractor control strategies. Efficient
    computational tools for studying SDs are essential for the understanding of Boolean
    attractor landscapes and connecting them to their biological functions.\r\nResults:
    We present a new approach to SD construction for asynchronously updated Boolean
    networks, implemented in the biologist’s Boolean attractor landscape mapper, biobalm.
    We compare biobalm to similar tools and find a substantial performance increase
    in SD construction, attractor identification, and attractor control. We perform
    the most comprehensive comparative analysis to date of the SD structure in experimentally-validated
    Boolean models of cell processes and random ensembles. We find that random models
    (including critical Kauffman networks) have relatively small SDs, indicating simple
    decision structures. In contrast, nonrandom models from the literature are enriched
    in extremely large SDs, indicating an abundance of decision points and suggesting
    the presence of complex Waddington landscapes in nature.\r\nAvailability and implementation:
    The tool biobalm is available online at https://github.com/jcrozum/biobalm. Further
    data, scripts for testing, analysis, and figure generation are available online
    at https://github.com/jcrozum/biobalm-analysis and in the reproducibility artefact
    at https://doi.org/10.5281/zenodo.13854760."
acknowledgement: V.-G.T. was supported by Institut Carnot STAR, Marseille, France.
  K.H.P. was supported by NSF grant MCB1715826 to Réka Albert. S.P. has received funding
  from the European Union’s Horizon 2020 Research and Innovation Programme under the
  Marie Sklodowska-Curie Grant Agreement No. 101034413. J.C.R. was supported by internal
  departmental funds provided by Luis M. Rocha. No funding bodies had any role in
  study design, analysis, decision to publish, or preparation of the article.
article_number: btaf280
article_processing_charge: Yes
article_type: original
author:
- first_name: Van Giang
  full_name: Trinh, Van Giang
  last_name: Trinh
- first_name: Kyu Hyong
  full_name: Park, Kyu Hyong
  last_name: Park
- first_name: Samuel
  full_name: Pastva, Samuel
  id: 07c5ea74-f61c-11ec-a664-aa7c5d957b2b
  last_name: Pastva
  orcid: 0000-0003-1993-0331
- first_name: Jordan C.
  full_name: Rozum, Jordan C.
  last_name: Rozum
citation:
  ama: Trinh VG, Park KH, Pastva S, Rozum JC. Mapping the attractor landscape of Boolean
    networks with biobalm. <i>Bioinformatics</i>. 2025;41(5). doi:<a href="https://doi.org/10.1093/bioinformatics/btaf280">10.1093/bioinformatics/btaf280</a>
  apa: Trinh, V. G., Park, K. H., Pastva, S., &#38; Rozum, J. C. (2025). Mapping the
    attractor landscape of Boolean networks with biobalm. <i>Bioinformatics</i>. Oxford
    University Press. <a href="https://doi.org/10.1093/bioinformatics/btaf280">https://doi.org/10.1093/bioinformatics/btaf280</a>
  chicago: Trinh, Van Giang, Kyu Hyong Park, Samuel Pastva, and Jordan C. Rozum. “Mapping
    the Attractor Landscape of Boolean Networks with Biobalm.” <i>Bioinformatics</i>.
    Oxford University Press, 2025. <a href="https://doi.org/10.1093/bioinformatics/btaf280">https://doi.org/10.1093/bioinformatics/btaf280</a>.
  ieee: V. G. Trinh, K. H. Park, S. Pastva, and J. C. Rozum, “Mapping the attractor
    landscape of Boolean networks with biobalm,” <i>Bioinformatics</i>, vol. 41, no.
    5. Oxford University Press, 2025.
  ista: Trinh VG, Park KH, Pastva S, Rozum JC. 2025. Mapping the attractor landscape
    of Boolean networks with biobalm. Bioinformatics. 41(5), btaf280.
  mla: Trinh, Van Giang, et al. “Mapping the Attractor Landscape of Boolean Networks
    with Biobalm.” <i>Bioinformatics</i>, vol. 41, no. 5, btaf280, Oxford University
    Press, 2025, doi:<a href="https://doi.org/10.1093/bioinformatics/btaf280">10.1093/bioinformatics/btaf280</a>.
  short: V.G. Trinh, K.H. Park, S. Pastva, J.C. Rozum, Bioinformatics 41 (2025).
corr_author: '1'
date_created: 2025-06-08T22:01:22Z
date_published: 2025-05-01T00:00:00Z
date_updated: 2025-09-30T12:46:33Z
day: '01'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1093/bioinformatics/btaf280
ec_funded: 1
external_id:
  isi:
  - '001493400600001'
  pmid:
  - '40327535'
file:
- access_level: open_access
  checksum: fa9d68aa0f5ce37598a623c9be936f09
  content_type: application/pdf
  creator: dernst
  date_created: 2025-06-10T07:07:45Z
  date_updated: 2025-06-10T07:07:45Z
  file_id: '19801'
  file_name: 2025_Bioinformatics_Trinh.pdf
  file_size: 2695801
  relation: main_file
  success: 1
file_date_updated: 2025-06-10T07:07:45Z
has_accepted_license: '1'
intvolume: '        41'
isi: 1
issue: '5'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
pmid: 1
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Bioinformatics
publication_identifier:
  eissn:
  - 1367-4811
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
related_material:
  link:
  - relation: software
    url: https://github.com/jcrozum/biobalm
  record:
  - id: '19800'
    relation: research_data
    status: public
scopus_import: '1'
status: public
title: Mapping the attractor landscape of Boolean networks with biobalm
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 41
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '19854'
abstract:
- lang: eng
  text: 'Asynchronous Boolean networks are a type of discrete dynamical system in
    which each variable can take one of two states, and a single variable state is
    updated in each time step according to pre-selected rules. Boolean networks are
    popular in systems biology due to their ability to model long-term biological
    phenotypes within a qualitative, predictive framework. Boolean networks model
    phenotypes as attractors, which are closely linked to minimal trap spaces (inescapable
    hypercubes in the system’s state space). In biological applications, attractors
    and minimal trap spaces are typically in one-to-one correspondence. However, this
    correspondence is not guaranteed: motif-avoidant attractors (MAAs) that lie outside
    minimal trap spaces are possible. MAAs are rare and poorly understood, despite
    recent efforts. In this contribution to the BMB & JMB Special Collection “Problems,
    Progress and Perspectives in Mathematical and Computational Biology”, we summarize
    the current state of knowledge regarding MAAs and present several novel observations
    regarding their response to node deletion reductions and linear extensions of
    edges. We conduct large-scale computational studies on an ensemble of 14 000 models
    derived from published Boolean models of biological systems, and more than 100
    million Random Boolean Networks. Our findings quantify the rarity of MAAs; in
    particular, we only observed MAAs in biological models after applying standard
    simplification methods, highlighting the role of network reduction in introducing
    MAAs into the dynamics. We also show that MAAs are fragile to linear extensions:
    in sparse networks, even a single linear node can disrupt virtually all MAAs.
    Motivated by this observation, we improve the upper bound on the number of delays
    needed to disrupt a motif-avoidant attractor.'
acknowledgement: Ondřej Huvar has been supported by the Czech Science Foundation grant
  No. GA22-10845S. Samuel Pastva received funding from the European Union’s Horizon
  2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement
  No. 101034413. Kyu Hyong Park and Réka Albert have been supported by NSF grant MCB
  1715826 and ARO grant 79961-SM-MUR. No funding bodies had any role in study design,
  analysis, decision to publish, or preparation of the manuscript.
article_number: '11'
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Samuel
  full_name: Pastva, Samuel
  id: 07c5ea74-f61c-11ec-a664-aa7c5d957b2b
  last_name: Pastva
  orcid: 0000-0003-1993-0331
- first_name: Kyu Hyong
  full_name: Park, Kyu Hyong
  last_name: Park
- first_name: Ondřej
  full_name: Huvar, Ondřej
  last_name: Huvar
- first_name: Jordan C.
  full_name: Rozum, Jordan C.
  last_name: Rozum
- first_name: Réka
  full_name: Albert, Réka
  last_name: Albert
citation:
  ama: 'Pastva S, Park KH, Huvar O, Rozum JC, Albert R. An open problem: Why are motif-avoidant
    attractors so rare in asynchronous Boolean networks? <i>Journal of Mathematical
    Biology</i>. 2025;91. doi:<a href="https://doi.org/10.1007/s00285-025-02235-8">10.1007/s00285-025-02235-8</a>'
  apa: 'Pastva, S., Park, K. H., Huvar, O., Rozum, J. C., &#38; Albert, R. (2025).
    An open problem: Why are motif-avoidant attractors so rare in asynchronous Boolean
    networks? <i>Journal of Mathematical Biology</i>. Springer Nature. <a href="https://doi.org/10.1007/s00285-025-02235-8">https://doi.org/10.1007/s00285-025-02235-8</a>'
  chicago: 'Pastva, Samuel, Kyu Hyong Park, Ondřej Huvar, Jordan C. Rozum, and Réka
    Albert. “An Open Problem: Why Are Motif-Avoidant Attractors so Rare in Asynchronous
    Boolean Networks?” <i>Journal of Mathematical Biology</i>. Springer Nature, 2025.
    <a href="https://doi.org/10.1007/s00285-025-02235-8">https://doi.org/10.1007/s00285-025-02235-8</a>.'
  ieee: 'S. Pastva, K. H. Park, O. Huvar, J. C. Rozum, and R. Albert, “An open problem:
    Why are motif-avoidant attractors so rare in asynchronous Boolean networks?,”
    <i>Journal of Mathematical Biology</i>, vol. 91. Springer Nature, 2025.'
  ista: 'Pastva S, Park KH, Huvar O, Rozum JC, Albert R. 2025. An open problem: Why
    are motif-avoidant attractors so rare in asynchronous Boolean networks? Journal
    of Mathematical Biology. 91, 11.'
  mla: 'Pastva, Samuel, et al. “An Open Problem: Why Are Motif-Avoidant Attractors
    so Rare in Asynchronous Boolean Networks?” <i>Journal of Mathematical Biology</i>,
    vol. 91, 11, Springer Nature, 2025, doi:<a href="https://doi.org/10.1007/s00285-025-02235-8">10.1007/s00285-025-02235-8</a>.'
  short: S. Pastva, K.H. Park, O. Huvar, J.C. Rozum, R. Albert, Journal of Mathematical
    Biology 91 (2025).
corr_author: '1'
date_created: 2025-06-22T22:02:05Z
date_published: 2025-06-12T00:00:00Z
date_updated: 2025-09-30T13:36:46Z
day: '12'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1007/s00285-025-02235-8
ec_funded: 1
external_id:
  arxiv:
  - '2410.03976'
  isi:
  - '001507009300001'
file:
- access_level: open_access
  checksum: a385ef2662f1d0c3497ed3f2721fe594
  content_type: application/pdf
  creator: dernst
  date_created: 2025-06-23T11:10:01Z
  date_updated: 2025-06-23T11:10:01Z
  file_id: '19871'
  file_name: 2025_JourMathBiology_Pastva.pdf
  file_size: 1243163
  relation: main_file
  success: 1
file_date_updated: 2025-06-23T11:10:01Z
has_accepted_license: '1'
intvolume: '        91'
isi: 1
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Journal of Mathematical Biology
publication_identifier:
  eissn:
  - 1432-1416
  issn:
  - 0303-6812
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'An open problem: Why are motif-avoidant attractors so rare in asynchronous
  Boolean networks?'
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 91
year: '2025'
...
---
_id: '18177'
abstract:
- lang: eng
  text: Partially Specified Boolean Networks (PSBNs) represent a family of Boolean
    models resulting from possible interpretations of unknown update logics. Hybrid
    extension of CTL (HCTL) has the power to express complex dynamical phenomena,
    such as oscillations or stability. We present BNClassifier to classify Boolean
    Networks corresponding to a given PSBN according to criteria specified in HCTL.
    The implementation of the tool is fully symbolic (based on BDDs). The results
    are visualised using the machine-learning-based technology of decision trees.
acknowledgement: The work has been supported by the Czech Science Foundation grant
  No. GA22-10845S. This project has received funding from the European Union’s Horizon
  2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement
  No. 101034413.
alternative_title:
- LNBI
article_processing_charge: No
author:
- first_name: Nikola
  full_name: Beneš, Nikola
  last_name: Beneš
- first_name: Luboš
  full_name: Brim, Luboš
  last_name: Brim
- first_name: Ondřej
  full_name: Huvar, Ondřej
  last_name: Huvar
- first_name: Samuel
  full_name: Pastva, Samuel
  id: 07c5ea74-f61c-11ec-a664-aa7c5d957b2b
  last_name: Pastva
  orcid: 0000-0003-1993-0331
- first_name: David
  full_name: Šafránek, David
  last_name: Šafránek
citation:
  ama: 'Beneš N, Brim L, Huvar O, Pastva S, Šafránek D. BNClassifier: Classifying
    boolean models by dynamic properties. In: <i>Computational Methods in Systems
    Biology</i>. Vol 14971. Springer Nature; 2024:19-26. doi:<a href="https://doi.org/10.1007/978-3-031-71671-3_2">10.1007/978-3-031-71671-3_2</a>'
  apa: 'Beneš, N., Brim, L., Huvar, O., Pastva, S., &#38; Šafránek, D. (2024). BNClassifier:
    Classifying boolean models by dynamic properties. In <i>Computational Methods
    in Systems Biology</i> (Vol. 14971, pp. 19–26). Springer Nature. <a href="https://doi.org/10.1007/978-3-031-71671-3_2">https://doi.org/10.1007/978-3-031-71671-3_2</a>'
  chicago: 'Beneš, Nikola, Luboš Brim, Ondřej Huvar, Samuel Pastva, and David Šafránek.
    “BNClassifier: Classifying Boolean Models by Dynamic Properties.” In <i>Computational
    Methods in Systems Biology</i>, 14971:19–26. Springer Nature, 2024. <a href="https://doi.org/10.1007/978-3-031-71671-3_2">https://doi.org/10.1007/978-3-031-71671-3_2</a>.'
  ieee: 'N. Beneš, L. Brim, O. Huvar, S. Pastva, and D. Šafránek, “BNClassifier: Classifying
    boolean models by dynamic properties,” in <i>Computational Methods in Systems
    Biology</i>, 2024, vol. 14971, pp. 19–26.'
  ista: 'Beneš N, Brim L, Huvar O, Pastva S, Šafránek D. 2024. BNClassifier: Classifying
    boolean models by dynamic properties. Computational Methods in Systems Biology.
    , LNBI, vol. 14971, 19–26.'
  mla: 'Beneš, Nikola, et al. “BNClassifier: Classifying Boolean Models by Dynamic
    Properties.” <i>Computational Methods in Systems Biology</i>, vol. 14971, Springer
    Nature, 2024, pp. 19–26, doi:<a href="https://doi.org/10.1007/978-3-031-71671-3_2">10.1007/978-3-031-71671-3_2</a>.'
  short: N. Beneš, L. Brim, O. Huvar, S. Pastva, D. Šafránek, in:, Computational Methods
    in Systems Biology, Springer Nature, 2024, pp. 19–26.
date_created: 2024-10-06T22:01:12Z
date_published: 2024-09-19T00:00:00Z
date_updated: 2025-09-08T09:54:27Z
day: '19'
department:
- _id: ToHe
doi: 10.1007/978-3-031-71671-3_2
ec_funded: 1
external_id:
  isi:
  - '001333144400002'
intvolume: '     14971'
isi: 1
language:
- iso: eng
month: '09'
oa_version: None
page: 19-26
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Computational Methods in Systems Biology
publication_identifier:
  eissn:
  - 1611-3349
  isbn:
  - '9783031716706'
  issn:
  - 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'BNClassifier: Classifying boolean models by dynamic properties'
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 14971
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '19800'
abstract:
- lang: eng
  text: "This archive contains all the code and data necessary to reproduce the results
    presented in the \r\n\"Mapping the attractor landscape of Boolean networks\" paper."
article_processing_charge: No
author:
- first_name: Van Giang
  full_name: trinh, Van Giang
  last_name: trinh
- first_name: Kyu Hyong
  full_name: Park, Kyu Hyong
  last_name: Park
- first_name: Samuel
  full_name: Pastva, Samuel
  id: 07c5ea74-f61c-11ec-a664-aa7c5d957b2b
  last_name: Pastva
  orcid: 0000-0003-1993-0331
- first_name: Jordan
  full_name: Rozum, Jordan
  last_name: Rozum
citation:
  ama: trinh VG, Park KH, Pastva S, Rozum J. Mapping the attractor landscape of Boolean
    networks. 2024. doi:<a href="https://doi.org/10.5281/ZENODO.13854759">10.5281/ZENODO.13854759</a>
  apa: trinh, V. G., Park, K. H., Pastva, S., &#38; Rozum, J. (2024). Mapping the
    attractor landscape of Boolean networks. Zenodo. <a href="https://doi.org/10.5281/ZENODO.13854759">https://doi.org/10.5281/ZENODO.13854759</a>
  chicago: trinh, Van Giang, Kyu Hyong Park, Samuel Pastva, and Jordan Rozum. “Mapping
    the Attractor Landscape of Boolean Networks.” Zenodo, 2024. <a href="https://doi.org/10.5281/ZENODO.13854759">https://doi.org/10.5281/ZENODO.13854759</a>.
  ieee: V. G. trinh, K. H. Park, S. Pastva, and J. Rozum, “Mapping the attractor landscape
    of Boolean networks.” Zenodo, 2024.
  ista: trinh VG, Park KH, Pastva S, Rozum J. 2024. Mapping the attractor landscape
    of Boolean networks, Zenodo, <a href="https://doi.org/10.5281/ZENODO.13854759">10.5281/ZENODO.13854759</a>.
  mla: trinh, Van Giang, et al. <i>Mapping the Attractor Landscape of Boolean Networks</i>.
    Zenodo, 2024, doi:<a href="https://doi.org/10.5281/ZENODO.13854759">10.5281/ZENODO.13854759</a>.
  short: V.G. trinh, K.H. Park, S. Pastva, J. Rozum, (2024).
date_created: 2025-06-10T07:10:01Z
date_published: 2024-09-28T00:00:00Z
date_updated: 2025-09-30T12:46:33Z
day: '28'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.5281/ZENODO.13854759
has_accepted_license: '1'
main_file_link:
- open_access: '1'
  url: https://doi.org/10.5281/zenodo.13854760
month: '09'
oa: 1
oa_version: Published Version
publisher: Zenodo
related_material:
  record:
  - id: '19796'
    relation: used_in_publication
    status: public
status: public
title: Mapping the attractor landscape of Boolean networks
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: research_data_reference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_id: '15321'
abstract:
- lang: eng
  text: Boolean Networks (BNs) are widely used as a modeling formalism in several
    domains, notably systems biology and computer science. A fundamental problem in
    BN analysis is the enumeration of trap spaces, which are hypercubes in the state
    space that cannot be escaped once entered. Several methods have been proposed
    for enumerating trap spaces, however they often suffer from scalability and efficiency
    issues, particularly for large and complex models. To our knowledge, the most
    efficient and recent methods for the trap space enumeration all rely on Answer
    Set Programming (ASP), which has been widely applied to the analysis of BNs. Motivated
    by these considerations, our work proposes a new method for enumerating trap spaces
    in BNs using ASP. We evaluate the method on a mix of 250+ real-world and 400+
    randomly generated BNs, showing that it enables analysis of models beyond the
    capabilities of existing tools (namely pyboolnet, mpbn, trappist, and trapmvn).
acknowledgement: This work was supported by Institut Carnot STAR, Marseille, France
  and by the European Union’s Horizon 2020 research and innovation programme under
  the Marie Skłodowska-Curie Grant Agreement No. 101034413.
article_processing_charge: No
author:
- first_name: Giang
  full_name: Trinh, Giang
  last_name: Trinh
- first_name: Belaid
  full_name: Benhamou, Belaid
  last_name: Benhamou
- first_name: Samuel
  full_name: Pastva, Samuel
  id: 07c5ea74-f61c-11ec-a664-aa7c5d957b2b
  last_name: Pastva
  orcid: 0000-0003-1993-0331
- first_name: Sylvain
  full_name: Soliman, Sylvain
  last_name: Soliman
citation:
  ama: 'Trinh G, Benhamou B, Pastva S, Soliman S. Scalable enumeration of trap spaces
    in boolean networks via answer set programming. In: <i>Proceedings of the 38th
    AAAI Conference on Artificial Intelligence</i>. Vol 38. Association for the Advancement
    of Artificial Intelligence; 2024:10714-10722. doi:<a href="https://doi.org/10.1609/aaai.v38i9.28943">10.1609/aaai.v38i9.28943</a>'
  apa: Trinh, G., Benhamou, B., Pastva, S., &#38; Soliman, S. (2024). Scalable enumeration
    of trap spaces in boolean networks via answer set programming. In <i>Proceedings
    of the 38th AAAI Conference on Artificial Intelligence</i> (Vol. 38, pp. 10714–10722).
    Association for the Advancement of Artificial Intelligence. <a href="https://doi.org/10.1609/aaai.v38i9.28943">https://doi.org/10.1609/aaai.v38i9.28943</a>
  chicago: Trinh, Giang, Belaid Benhamou, Samuel Pastva, and Sylvain Soliman. “Scalable
    Enumeration of Trap Spaces in Boolean Networks via Answer Set Programming.” In
    <i>Proceedings of the 38th AAAI Conference on Artificial Intelligence</i>, 38:10714–22.
    Association for the Advancement of Artificial Intelligence, 2024. <a href="https://doi.org/10.1609/aaai.v38i9.28943">https://doi.org/10.1609/aaai.v38i9.28943</a>.
  ieee: G. Trinh, B. Benhamou, S. Pastva, and S. Soliman, “Scalable enumeration of
    trap spaces in boolean networks via answer set programming,” in <i>Proceedings
    of the 38th AAAI Conference on Artificial Intelligence</i>, 2024, vol. 38, no.
    9, pp. 10714–10722.
  ista: Trinh G, Benhamou B, Pastva S, Soliman S. 2024. Scalable enumeration of trap
    spaces in boolean networks via answer set programming. Proceedings of the 38th
    AAAI Conference on Artificial Intelligence. vol. 38, 10714–10722.
  mla: Trinh, Giang, et al. “Scalable Enumeration of Trap Spaces in Boolean Networks
    via Answer Set Programming.” <i>Proceedings of the 38th AAAI Conference on Artificial
    Intelligence</i>, vol. 38, no. 9, Association for the Advancement of Artificial
    Intelligence, 2024, pp. 10714–22, doi:<a href="https://doi.org/10.1609/aaai.v38i9.28943">10.1609/aaai.v38i9.28943</a>.
  short: G. Trinh, B. Benhamou, S. Pastva, S. Soliman, in:, Proceedings of the 38th
    AAAI Conference on Artificial Intelligence, Association for the Advancement of
    Artificial Intelligence, 2024, pp. 10714–10722.
date_created: 2024-04-14T22:01:02Z
date_published: 2024-03-25T00:00:00Z
date_updated: 2025-04-14T07:54:55Z
day: '25'
department:
- _id: ToHe
doi: 10.1609/aaai.v38i9.28943
ec_funded: 1
intvolume: '        38'
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://amu.hal.science/hal-04523118/
month: '03'
oa: 1
oa_version: Published Version
page: 10714-10722
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Proceedings of the 38th AAAI Conference on Artificial Intelligence
publication_identifier:
  eissn:
  - 2374-3468
  isbn:
  - '1577358872'
  issn:
  - 2159-5399
publication_status: published
publisher: Association for the Advancement of Artificial Intelligence
quality_controlled: '1'
scopus_import: '1'
status: public
title: Scalable enumeration of trap spaces in boolean networks via answer set programming
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 38
year: '2024'
...
---
_id: '14411'
abstract:
- lang: eng
  text: "Partially specified Boolean networks (PSBNs) represent a promising framework
    for the qualitative modelling of biological systems in which the logic of interactions
    is not completely known. Phenotype control aims to stabilise the network in states
    exhibiting specific traits.\r\nIn this paper, we define the phenotype control
    problem in the context of asynchronous PSBNs and propose a novel semi-symbolic
    algorithm for solving this problem with permanent variable perturbations."
acknowledgement: This work was supported by the Czech Foundation grant No. GA22-10845S,
  Grant Agency of Masaryk University grant No. MUNI/G/1771/2020, and the European
  Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
  Grant Agreement No. 101034413.
alternative_title:
- LNBI
article_processing_charge: No
author:
- first_name: Nikola
  full_name: Beneš, Nikola
  last_name: Beneš
- first_name: Luboš
  full_name: Brim, Luboš
  last_name: Brim
- first_name: Samuel
  full_name: Pastva, Samuel
  id: 07c5ea74-f61c-11ec-a664-aa7c5d957b2b
  last_name: Pastva
  orcid: 0000-0003-1993-0331
- first_name: David
  full_name: Šafránek, David
  last_name: Šafránek
- first_name: Eva
  full_name: Šmijáková, Eva
  last_name: Šmijáková
citation:
  ama: 'Beneš N, Brim L, Pastva S, Šafránek D, Šmijáková E. Phenotype control of partially
    specified boolean networks. In: <i>21st International Conference on Computational
    Methods in Systems Biology</i>. Vol 14137. Springer Nature; 2023:18-35. doi:<a
    href="https://doi.org/10.1007/978-3-031-42697-1_2">10.1007/978-3-031-42697-1_2</a>'
  apa: 'Beneš, N., Brim, L., Pastva, S., Šafránek, D., &#38; Šmijáková, E. (2023).
    Phenotype control of partially specified boolean networks. In <i>21st International
    Conference on Computational Methods in Systems Biology</i> (Vol. 14137, pp. 18–35).
    Luxembourg City, Luxembourg: Springer Nature. <a href="https://doi.org/10.1007/978-3-031-42697-1_2">https://doi.org/10.1007/978-3-031-42697-1_2</a>'
  chicago: Beneš, Nikola, Luboš Brim, Samuel Pastva, David Šafránek, and Eva Šmijáková.
    “Phenotype Control of Partially Specified Boolean Networks.” In <i>21st International
    Conference on Computational Methods in Systems Biology</i>, 14137:18–35. Springer
    Nature, 2023. <a href="https://doi.org/10.1007/978-3-031-42697-1_2">https://doi.org/10.1007/978-3-031-42697-1_2</a>.
  ieee: N. Beneš, L. Brim, S. Pastva, D. Šafránek, and E. Šmijáková, “Phenotype control
    of partially specified boolean networks,” in <i>21st International Conference
    on Computational Methods in Systems Biology</i>, Luxembourg City, Luxembourg,
    2023, vol. 14137, pp. 18–35.
  ista: 'Beneš N, Brim L, Pastva S, Šafránek D, Šmijáková E. 2023. Phenotype control
    of partially specified boolean networks. 21st International Conference on Computational
    Methods in Systems Biology. CMSB: Computational Methods in Systems Biology, LNBI,
    vol. 14137, 18–35.'
  mla: Beneš, Nikola, et al. “Phenotype Control of Partially Specified Boolean Networks.”
    <i>21st International Conference on Computational Methods in Systems Biology</i>,
    vol. 14137, Springer Nature, 2023, pp. 18–35, doi:<a href="https://doi.org/10.1007/978-3-031-42697-1_2">10.1007/978-3-031-42697-1_2</a>.
  short: N. Beneš, L. Brim, S. Pastva, D. Šafránek, E. Šmijáková, in:, 21st International
    Conference on Computational Methods in Systems Biology, Springer Nature, 2023,
    pp. 18–35.
conference:
  end_date: 2023-09-15
  location: Luxembourg City, Luxembourg
  name: 'CMSB: Computational Methods in Systems Biology'
  start_date: 2023-09-13
date_created: 2023-10-08T22:01:18Z
date_published: 2023-09-09T00:00:00Z
date_updated: 2025-09-09T14:25:46Z
day: '09'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1007/978-3-031-42697-1_2
ec_funded: 1
external_id:
  isi:
  - '001156280600002'
file:
- access_level: open_access
  checksum: 6f71bdaedb770b52380222fd9f4d7937
  content_type: application/pdf
  creator: spastva
  date_created: 2024-02-16T08:26:32Z
  date_updated: 2024-02-16T08:26:32Z
  file_id: '14997'
  file_name: cmsb2023.pdf
  file_size: 691582
  relation: main_file
  success: 1
file_date_updated: 2024-02-16T08:26:32Z
has_accepted_license: '1'
intvolume: '     14137'
isi: 1
language:
- iso: eng
month: '09'
oa: 1
oa_version: Submitted Version
page: 18-35
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: 21st International Conference on Computational Methods in Systems Biology
publication_identifier:
  eissn:
  - 1611-3349
  isbn:
  - '9783031426964'
  issn:
  - 0302-9743
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Phenotype control of partially specified boolean networks
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 14137
year: '2023'
...
---
_id: '14718'
abstract:
- lang: eng
  text: 'Binary decision diagrams (BDDs) are one of the fundamental data structures
    in formal methods and computer science in general. However, the performance of
    BDD-based algorithms greatly depends on memory latency due to the reliance on
    large hash tables and thus, by extension, on the speed of random memory access.
    This hinders the full utilisation of resources available on modern CPUs, since
    the absolute memory latency has not improved significantly for at least a decade.
    In this paper, we explore several implementation techniques that improve the performance
    of BDD manipulation either through enhanced memory locality or by partially eliminating
    random memory access. On a benchmark suite of 600+ BDDs derived from real-world
    applications, we demonstrate runtime that is comparable or better than parallelising
    the same operations on eight CPU cores. '
acknowledgement: "This work was supported by the European Union’s Horizon 2020 research
  and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413
  and the\r\n“VAMOS” grant ERC-2020-AdG 101020093."
article_processing_charge: No
author:
- first_name: Samuel
  full_name: Pastva, Samuel
  id: 07c5ea74-f61c-11ec-a664-aa7c5d957b2b
  last_name: Pastva
  orcid: 0000-0003-1993-0331
- first_name: Thomas A
  full_name: Henzinger, Thomas A
  id: 40876CD8-F248-11E8-B48F-1D18A9856A87
  last_name: Henzinger
  orcid: 0000-0002-2985-7724
citation:
  ama: 'Pastva S, Henzinger TA. Binary decision diagrams on modern hardware. In: <i>Proceedings
    of the 23rd Conference on Formal Methods in Computer-Aided Design</i>. TU Vienna
    Academic Press; 2023:122-131. doi:<a href="https://doi.org/10.34727/2023/isbn.978-3-85448-060-0_20">10.34727/2023/isbn.978-3-85448-060-0_20</a>'
  apa: 'Pastva, S., &#38; Henzinger, T. A. (2023). Binary decision diagrams on modern
    hardware. In <i>Proceedings of the 23rd Conference on Formal Methods in Computer-Aided
    Design</i> (pp. 122–131). Ames, IA, United States: TU Vienna Academic Press. <a
    href="https://doi.org/10.34727/2023/isbn.978-3-85448-060-0_20">https://doi.org/10.34727/2023/isbn.978-3-85448-060-0_20</a>'
  chicago: Pastva, Samuel, and Thomas A Henzinger. “Binary Decision Diagrams on Modern
    Hardware.” In <i>Proceedings of the 23rd Conference on Formal Methods in Computer-Aided
    Design</i>, 122–31. TU Vienna Academic Press, 2023. <a href="https://doi.org/10.34727/2023/isbn.978-3-85448-060-0_20">https://doi.org/10.34727/2023/isbn.978-3-85448-060-0_20</a>.
  ieee: S. Pastva and T. A. Henzinger, “Binary decision diagrams on modern hardware,”
    in <i>Proceedings of the 23rd Conference on Formal Methods in Computer-Aided Design</i>,
    Ames, IA, United States, 2023, pp. 122–131.
  ista: 'Pastva S, Henzinger TA. 2023. Binary decision diagrams on modern hardware.
    Proceedings of the 23rd Conference on Formal Methods in Computer-Aided Design.
    FMCAD: Formal Methods in Computer-Aided Design, 122–131.'
  mla: Pastva, Samuel, and Thomas A. Henzinger. “Binary Decision Diagrams on Modern
    Hardware.” <i>Proceedings of the 23rd Conference on Formal Methods in Computer-Aided
    Design</i>, TU Vienna Academic Press, 2023, pp. 122–31, doi:<a href="https://doi.org/10.34727/2023/isbn.978-3-85448-060-0_20">10.34727/2023/isbn.978-3-85448-060-0_20</a>.
  short: S. Pastva, T.A. Henzinger, in:, Proceedings of the 23rd Conference on Formal
    Methods in Computer-Aided Design, TU Vienna Academic Press, 2023, pp. 122–131.
conference:
  end_date: 2023-10-27
  location: Ames, IA, United States
  name: 'FMCAD: Formal Methods in Computer-Aided Design'
  start_date: 2023-10-25
corr_author: '1'
date_created: 2023-12-31T23:01:03Z
date_published: 2023-10-01T00:00:00Z
date_updated: 2025-09-09T14:04:14Z
day: '01'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.34727/2023/isbn.978-3-85448-060-0_20
ec_funded: 1
external_id:
  isi:
  - '001504402400020'
file:
- access_level: open_access
  checksum: 818d6e13dd508f3a04f0941081022e5d
  content_type: application/pdf
  creator: dernst
  date_created: 2024-01-02T08:14:23Z
  date_updated: 2024-01-02T08:14:23Z
  file_id: '14721'
  file_name: 2023_FMCAD_Pastva.pdf
  file_size: 524321
  relation: main_file
  success: 1
file_date_updated: 2024-01-02T08:14:23Z
has_accepted_license: '1'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 122-131
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
- _id: 62781420-2b32-11ec-9570-8d9b63373d4d
  call_identifier: H2020
  grant_number: '101020093'
  name: Vigilant Algorithmic Monitoring of Software
publication: Proceedings of the 23rd Conference on Formal Methods in Computer-Aided
  Design
publication_identifier:
  isbn:
  - '9783854480600'
publication_status: published
publisher: TU Vienna Academic Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Binary decision diagrams on modern hardware
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2023'
...
---
_id: '12876'
abstract:
- lang: eng
  text: "Motivation: The problem of model inference is of fundamental importance to
    systems biology. Logical models (e.g. Boolean networks; BNs) represent a computationally
    attractive approach capable of handling large biological networks. The models
    are typically inferred from experimental data. However, even with a substantial
    amount of experimental data supported by some prior knowledge, existing inference
    methods often focus on a small sample of admissible candidate models only.\r\n\r\nResults:
    We propose Boolean network sketches as a new formal instrument for the inference
    of Boolean networks. A sketch integrates (typically partial) knowledge about the
    network’s topology and the update logic (obtained through, e.g. a biological knowledge
    base or a literature search), as well as further assumptions about the properties
    of the network’s transitions (e.g. the form of its attractor landscape), and additional
    restrictions on the model dynamics given by the measured experimental data. Our
    new BNs inference algorithm starts with an ‘initial’ sketch, which is extended
    by adding restrictions representing experimental data to a ‘data-informed’ sketch
    and subsequently computes all BNs consistent with the data-informed sketch. Our
    algorithm is based on a symbolic representation and coloured model-checking. Our
    approach is unique in its ability to cover a broad spectrum of knowledge and efficiently
    produce a compact representation of all inferred BNs. We evaluate the method on
    a non-trivial collection of real-world and simulated data."
acknowledgement: This work was partially supported by GACR [grant No. GA22-10845S];
  and Grant Agency of Masaryk University [grant No. MUNI/G/1771/2020]. This work was
  partially supported by European Union’s Horizon 2020 research and innovation programme
  under the Marie Skłodowska-Curie [Grant Agreement No. 101034413 to S.P.].
article_number: btad158
article_processing_charge: No
article_type: original
author:
- first_name: Nikola
  full_name: Beneš, Nikola
  last_name: Beneš
- first_name: Luboš
  full_name: Brim, Luboš
  last_name: Brim
- first_name: Ondřej
  full_name: Huvar, Ondřej
  last_name: Huvar
- first_name: Samuel
  full_name: Pastva, Samuel
  id: 07c5ea74-f61c-11ec-a664-aa7c5d957b2b
  last_name: Pastva
  orcid: 0000-0003-1993-0331
- first_name: David
  full_name: Šafránek, David
  last_name: Šafránek
citation:
  ama: 'Beneš N, Brim L, Huvar O, Pastva S, Šafránek D. Boolean network sketches:
    A unifying framework for logical model inference. <i>Bioinformatics</i>. 2023;39(4).
    doi:<a href="https://doi.org/10.1093/bioinformatics/btad158">10.1093/bioinformatics/btad158</a>'
  apa: 'Beneš, N., Brim, L., Huvar, O., Pastva, S., &#38; Šafránek, D. (2023). Boolean
    network sketches: A unifying framework for logical model inference. <i>Bioinformatics</i>.
    Oxford University Press. <a href="https://doi.org/10.1093/bioinformatics/btad158">https://doi.org/10.1093/bioinformatics/btad158</a>'
  chicago: 'Beneš, Nikola, Luboš Brim, Ondřej Huvar, Samuel Pastva, and David Šafránek.
    “Boolean Network Sketches: A Unifying Framework for Logical Model Inference.”
    <i>Bioinformatics</i>. Oxford University Press, 2023. <a href="https://doi.org/10.1093/bioinformatics/btad158">https://doi.org/10.1093/bioinformatics/btad158</a>.'
  ieee: 'N. Beneš, L. Brim, O. Huvar, S. Pastva, and D. Šafránek, “Boolean network
    sketches: A unifying framework for logical model inference,” <i>Bioinformatics</i>,
    vol. 39, no. 4. Oxford University Press, 2023.'
  ista: 'Beneš N, Brim L, Huvar O, Pastva S, Šafránek D. 2023. Boolean network sketches:
    A unifying framework for logical model inference. Bioinformatics. 39(4), btad158.'
  mla: 'Beneš, Nikola, et al. “Boolean Network Sketches: A Unifying Framework for
    Logical Model Inference.” <i>Bioinformatics</i>, vol. 39, no. 4, btad158, Oxford
    University Press, 2023, doi:<a href="https://doi.org/10.1093/bioinformatics/btad158">10.1093/bioinformatics/btad158</a>.'
  short: N. Beneš, L. Brim, O. Huvar, S. Pastva, D. Šafránek, Bioinformatics 39 (2023).
date_created: 2023-04-30T22:01:05Z
date_published: 2023-04-03T00:00:00Z
date_updated: 2025-05-14T11:06:50Z
day: '03'
ddc:
- '000'
department:
- _id: ToHe
doi: 10.1093/bioinformatics/btad158
ec_funded: 1
external_id:
  isi:
  - '000976610800001'
  pmid:
  - '37004199'
file:
- access_level: open_access
  checksum: 2cb90ddf781baefddf47eac4b54e2a03
  content_type: application/pdf
  creator: dernst
  date_created: 2023-05-02T07:39:04Z
  date_updated: 2023-05-02T07:39:04Z
  file_id: '12886'
  file_name: 2023_Bioinformatics_Benes.pdf
  file_size: 478740
  relation: main_file
  success: 1
file_date_updated: 2023-05-02T07:39:04Z
has_accepted_license: '1'
intvolume: '        39'
isi: 1
issue: '4'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
pmid: 1
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Bioinformatics
publication_identifier:
  eissn:
  - 1367-4811
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
related_material:
  link:
  - relation: software
    url: https://doi.org/10.5281/zenodo.7688740
scopus_import: '1'
status: public
title: 'Boolean network sketches: A unifying framework for logical model inference'
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 39
year: '2023'
...
---
_id: '13263'
abstract:
- lang: eng
  text: "Motivation: Boolean networks are simple but efficient mathematical formalism
    for modelling complex biological systems. However, having only two levels of activation
    is sometimes not enough to fully capture the dynamics of real-world biological
    systems. Hence, the need for multi-valued networks (MVNs), a generalization of
    Boolean networks. Despite the importance of MVNs for modelling biological systems,
    only limited progress has been made on developing theories, analysis methods,
    and tools that can support them. In particular, the recent use of trap spaces
    in Boolean networks made a great impact on the field of systems biology, but there
    has been no similar concept defined and studied for MVNs to date.\r\n\r\nResults:
    In this work, we generalize the concept of trap spaces in Boolean networks to
    that in MVNs. We then develop the theory and the analysis methods for trap spaces
    in MVNs. In particular, we implement all proposed methods in a Python package
    called trapmvn. Not only showing the applicability of our approach via a realistic
    case study, we also evaluate the time efficiency of the method on a large collection
    of real-world models. The experimental results confirm the time efficiency, which
    we believe enables more accurate analysis on larger and more complex multi-valued
    models."
acknowledgement: This work was supported by L’Institut Carnot STAR, Marseille, France,
  and by the European Union’s Horizon 2020 research and innovation programme under
  the Marie Skłodowska-Curie Grant Agreement No. [101034413].
article_processing_charge: Yes
article_type: original
author:
- first_name: Van Giang
  full_name: Trinh, Van Giang
  last_name: Trinh
- first_name: Belaid
  full_name: Benhamou, Belaid
  last_name: Benhamou
- first_name: Thomas A
  full_name: Henzinger, Thomas A
  id: 40876CD8-F248-11E8-B48F-1D18A9856A87
  last_name: Henzinger
  orcid: 0000-0002-2985-7724
- first_name: Samuel
  full_name: Pastva, Samuel
  id: 07c5ea74-f61c-11ec-a664-aa7c5d957b2b
  last_name: Pastva
  orcid: 0000-0003-1993-0331
citation:
  ama: 'Trinh VG, Benhamou B, Henzinger TA, Pastva S. Trap spaces of multi-valued
    networks: Definition, computation, and applications. <i>Bioinformatics</i>. 2023;39(Supplement_1):i513-i522.
    doi:<a href="https://doi.org/10.1093/bioinformatics/btad262">10.1093/bioinformatics/btad262</a>'
  apa: 'Trinh, V. G., Benhamou, B., Henzinger, T. A., &#38; Pastva, S. (2023). Trap
    spaces of multi-valued networks: Definition, computation, and applications. <i>Bioinformatics</i>.
    Oxford University Press. <a href="https://doi.org/10.1093/bioinformatics/btad262">https://doi.org/10.1093/bioinformatics/btad262</a>'
  chicago: 'Trinh, Van Giang, Belaid Benhamou, Thomas A Henzinger, and Samuel Pastva.
    “Trap Spaces of Multi-Valued Networks: Definition, Computation, and Applications.”
    <i>Bioinformatics</i>. Oxford University Press, 2023. <a href="https://doi.org/10.1093/bioinformatics/btad262">https://doi.org/10.1093/bioinformatics/btad262</a>.'
  ieee: 'V. G. Trinh, B. Benhamou, T. A. Henzinger, and S. Pastva, “Trap spaces of
    multi-valued networks: Definition, computation, and applications,” <i>Bioinformatics</i>,
    vol. 39, no. Supplement_1. Oxford University Press, pp. i513–i522, 2023.'
  ista: 'Trinh VG, Benhamou B, Henzinger TA, Pastva S. 2023. Trap spaces of multi-valued
    networks: Definition, computation, and applications. Bioinformatics. 39(Supplement_1),
    i513–i522.'
  mla: 'Trinh, Van Giang, et al. “Trap Spaces of Multi-Valued Networks: Definition,
    Computation, and Applications.” <i>Bioinformatics</i>, vol. 39, no. Supplement_1,
    Oxford University Press, 2023, pp. i513–22, doi:<a href="https://doi.org/10.1093/bioinformatics/btad262">10.1093/bioinformatics/btad262</a>.'
  short: V.G. Trinh, B. Benhamou, T.A. Henzinger, S. Pastva, Bioinformatics 39 (2023)
    i513–i522.
corr_author: '1'
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title: 'Trap spaces of multi-valued networks: Definition, computation, and applications'
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...
