Must-read papers on Brain Control Analysis

Papers about the theory and application of brain control theory. Contributed by Shikuang Deng, Shi Gu.


1. Survey
2. General Theory
2.1 Controllability2.2 Control Set
2.3 Control Energy2.4 Observability
2.5 Optimal Control2.6 Temporal Control
3. Brain Control Analysis
3.1 Review
3.2 Structural Controllability
3.2.1 Brain Advantage3.2.2 Control Radius
3.2.3 Stimulation
3.3 Control Set and Energy
3.3.1 Control Set3.3.2 State Transition
3.4 Applications
3.4.1 Cognition3.4.2 Development and Heritability
3.4.3 Disease

General Theory


  1. Controllability of complex networks. nature, 2011. paper

    Liu Y Y, Slotine J J, Barab$\mathrm{\acute{\textit{a}}}$si A L.

  2. Optimizing controllability of complex networks by minimum structural perturbations. Physical Review E, 2012. paper
    Wang W X, Ni X, Lai Y C, et al.

  3. Intrinsic dynamics induce global symmetry in network controllability. Scientific reports, 2015. paper
    Zhao C, Wang W X, Liu Y Y, et al.

  4. Control principles of complex systems. Reviews of Modern Physics, 2016. paper
    Liu Y Y, Barab$\mathrm{\acute{\textit{a}}}$si A L.

  5. Controlling network dynamics. arXiv preprint, 2020. paper
    Aming Li, Yang-Yu Liu

Control Set

  1. Control centrality and hierarchical structure in complex networks. Plos one, 2012. paper
    Liu Y Y, Slotine J J, Barab$\mathrm{\acute{\textit{a}}}$si A L.

  2. Emergence of bimodality in controlling complex networks. Nature communications, 2013. paper
    Jia T, Liu Y Y, Cs$\mathrm{\acute{\textit{o}}}$ka E, et al.

  3. Effect of correlations on network controllability Scientific reports, 2013. paper
    P$\mathrm{\acute{\textit{o}}}$sfai M, Liu Y Y, Slotine J J, et al.

  4. Target control of complex networks. Nature communications, 2014. paper
    Gao J, Liu Y Y, D’souza R M, et al.

Control Energy

  1. Controllability metrics, limitations and algorithms for complex networks. IEEE Transactions on Control of Network Systems, 2014. paper
    Pasqualetti F, Zampieri S, Bullo F.

  2. Spectrum of controlling and observing complex networks. Nature Physics, 2015. paper
    Yan G, Tsekenis G, Barzel B, et al.

  3. Control energy scaling in temporal networks. arXiv preprint, 2017. paper
    Li A, Cornelius S P, Liu Y Y, et al.

  4. Energy cost for controlling complex networks with linear dynamics. Physical Review E, 2019. paper
    Duan G, Li A, Meng T, et al.

  5. Upper bound of the minimum energy cost for controlling complex networks. IEEE, 2019. paper
    Duan G, Li A, Meng T, et al.


  1. Observability of complex systems. Proceedings of the National Academy of Sciences, 2013. paper
    Liu Y Y, Slotine J J, Barab$\mathrm{\acute{\textit{a}}}$si A L.

Optimal Control

  1. The optimal trajectory to control complex networks. arXiv preprint, 2018. paper
    Li A, Wang L, Schweitzer F.

Temporal Control

  1. The fundamental advantages of temporal networks. Science, 2017. paper
    Li A, Cornelius S P, Liu Y Y, et al.

Brain Control Analysis


  1. Brain and cognitive reserve: translation via network control theory. Neuroscience & Biobehavioral Reviews, 2017. paper
    Medaglia J D, Pasqualetti F, Hamilton R H, et al.

  2. A practical guide to methodological considerations in the controllability of structural brain networks. arXiv preprint, 2019. paper
    Karrer T M, Kim J Z, Stiso J, et al.

  3. The physics of brain network structure, function and control. Nature Reviews Physics, 2019. paper
    Lynn C W, Bassett D S.

Structural Controllability

  1. Controllability of structural brain networks. Nature communications, 2015. paper
    Gu S, Pasqualetti F, Cieslak M, et al.

  2. On structural controllability of symmetric (brain) networks. arXiv preprint, 2017. paper
    Menara T, Gu S, Bassett D S, et al.

  3. Models of communication and control for brain networks: distinctions, convergence, and future outlook. arXiv preprint, 2020. paper
    Srivastava P, Nozari E, Kim J Z, et al.

  4. Control of brain network dynamics across diverse scales of space and time. Physical Review E, 2020. paper
    Tang E, Ju H, Baum G L, et al.

Brain Advantage

  1. Role of graph architecture in controlling dynamical networks with applications to neural systems. Nature physics, 2018. paper
    Kim J Z, Soffer J M, Kahn A E, et al.
  2. Benchmarking measures of network controllability on canonical graph models. Journal of Nonlinear Science, 2018. paper
    Wu-Yan E, Betzel R F, Tang E, et al.

Control Radius

  1. The structured controllability radius of symmetric (brain) networks. IEEE, 2018. paper
    Menara T, Katewa V, Bassett D S, et al.


  1. Stimulation-based control of dynamic brain networks. PLoS computational biology, 2016. paper
    Muldoon S F, Pasqualetti F, Gu S, et al.

  2. Predictive control of electrophysiological network architecture using direct, single-node neurostimulation in humans. Biorxiv, 2018. paper
    Khambhati A N, Kahn A E, Costantini J, et al.

  3. Functional control of electrophysiological network architecture using direct neurostimulation in humans. Network Neuroscience, 2019. paper
    Khambhati A N, Kahn A E, Costantini J, et al.

Control Set and Energy

Control Set

  1. Topological principles of control in dynamical network systems. arXiv preprint, 2017. paper
    Kim J, Soffer J M, Kahn A E, et al.

  2. Data-Driven Control of Complex Networks. arXiv preprint, 2020. paper
    Baggio G, Bassett D S, Pasqualetti F.

State Transition

  1. Linear dynamics & control of brain networks. arXiv preprint, 2019. paper
    Kim J Z, Bassett D S.

  2. Optimally controlling the human connectome: the role of network topology. Scientific reports, 2016. paper
    Betzel R F, Gu S, Medaglia J D, et al.



  1. Cognitive control in the controllable connectome. arXiv preprint, 2016.paper
    Medaglia J D, Gu S, Pasqualetti F, et al.

  2. Context-dependent architecture of brain state dynamics is explained by white matter connectivity and theories of network control. arXiv preprint, 2018. paper
    Cornblath E J, Ashourvan A, Kim J Z, et al.

  3. Network controllability in the inferior frontal gyrus relates to controlled language variability and susceptibility to TMS. Journal of Neuroscience, 2018. paper
    Medaglia J D, Harvey D Y, White N, et al.

  4. Brain state stability during working memory is explained by network control theory, modulated by dopamine D1/D2 receptor function, and diminished in schizophrenia. arXiv preprint, 2019. paper
    Braun U, Harneit A, Pergola G, et al.

Development and Heritability

  1. Developmental increases in white matter network controllability support a growing diversity of brain dynamics. Nature communications, 2017. paper
    Tang E, Giusti C, Baum G L, et al.

  2. Heritability and cognitive relevance of structural brain controllability. Cerebral Cortex, 2020. paper
    Lee W H, Rodrigue A, Glahn D C, et al.


  1. Fronto-limbic dysconnectivity leads to impaired brain network controllability in young people with bipolar disorder and those at high genetic risk. NeuroImage: Clinical, 2018. paper
    Jeganathan J, Perry A, Bassett D S, et al.

  2. Structural control energy of resting-state functional brain states reveals inefficient brain dynamics in psychosis vulnerability. bioRxiv, 2019. paper
    Zoeller D, Sandini C, Schaer M, et al.

  3. Model-based design for seizure control by stimulation. Journal of Neural Engineering, 2020. paper
    Ashourvan A, Pequito S, Khambhati A N, et al.

  4. Time-evolving controllability of effective connectivity networks during seizure progression. arXiv preprint, 2020. paper
    Scheid B H, Ashourvan A, Stiso J, et al.

Shi Gu (顾实)
Shi Gu (顾实)
Professor of Computer Science

My research interests include computational neuroscience and machine learning.