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Must-read papers on Brain Control Analysis

6 minute read


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, Barabási 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, Barabási 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, Barabási A L.
  2. Emergence of bimodality in controlling complex networks. Nature communications, 2013. paper
    Jia T, Liu Y Y, Csóka E, et al.
  3. Effect of correlations on network controllability Scientific reports, 2013. paper
    Pósfai 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, Barabási 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.
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Welcome to join us!

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Welcome to join our Brain & Intelligence Laboratory at University of Electronic Science and Technology of China!

Open Positions:

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Controllability of structural brain networks

Published in Nature Communications, 2015

Cognitive function is driven by dynamic interactions between large-scale neural circuits or networks, enabling behaviour. However, fundamental principles constraining these dynamic network processes have remained elusive. Read more

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The Re-evolution of Human Brain


Professor Gu works for School of Computer Science and Engineering in UESTC, and he holds a PhD in Applied Mathematics and Computational Science from University of Pennsylvania, and has been the candidate of Thirteenth Batch of National 1000 People Project Youth Program. He put forward a control model of brain network, established a link between brain network cognitive control and engineering control model, which provides a feasible new idea for understanding the brain cognitive control function and gains pioneering theoretical achievements, and resulting in a profound significance for intelligent control model. Also being an neurotic system development researchers, he will lead us to explore the frontiers of human potential development. Read more

Functional Controllability on Brain Networks


In recent years, both network neuroscience and cognitive science have developed vigorously. The network approach provides an analytical perspective of understanding the brain structures and functions, and uncovers the intrinsic correlation between them. However, this family of methods pays more attention on the discovery and pattern recognition in the phenomenon, thus lack a mechanistic explanation of why and how this correlation happens. Read more

Multi-object optimization on structural and functional community structures


Human brain is a complex system displaying modular characteristics in both structural and functional networks. Although coupled on a certain level, such two types of modular structures remain different in principle where the structural modules provide disciplines of anatomical organization, while the functional modules reflect the assembling principles of statistical association. Read more


Introduction to Network Neuroscience and Artificial Intelligence

Undergraduate course, UESTC, Computer Science, 2019

Network science is an interdisciplinary field that focuses on the networked objects in physical world, biological systems and social phenomenon. It builds predictive models with properties from the perspective of complex network to investigate problems in information network, internet network, biological network, learning and cognitive network, and social network. This course consists of two sections. In the first section, we will introduce the general theory of complex network. In the second section, we will introduce how to apply the network theory as well as other data mining methods to perform analyses in brain science, and how to understand the principles of brain organization and function. Throughout the learning of this course, we hope that the students can have a glimpse of the frontier of network neuroscience and get familiar of the paradigm of research. Read more