Boards, Advisory Committees, Professional Organizations

  • Member, Society for Industrial and Applied Mathematics (2017 - Present)
  • Member, Society for Neuroscience (2014 - Present)

Professional Education

  • Bachelor of Science, Peking University (2011)
  • Doctor of Philosophy, Florida Atlantic University (2018)
  • Master of Science, University of Pennsylvania (2012)

Stanford Advisors


All Publications

  • Topological portraits of multiscale coordination dynamics. Journal of neuroscience methods Zhang, M., Kalies, W. D., Kelso, J. A., Tognoli, E. 2020: 108672


    Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a challenge in both theoretical and empirical realms. The present work shows how integrating approaches from computational algebraic topology and dynamical systems may help us meet this challenge. In particular, we focus on the application of multiscale topological analysis to coordinated rhythmic processes. First, theoretical arguments are introduced as to why certain topological features and their scale-dependency are highly relevant to understanding complex collective dynamics. Second, we propose a method to capture such dynamically relevant topological information using persistent homology, which allows us to effectively construct a multiscale topological portrait of rhythmic coordination. Finally, the method is put to test in detecting transitions in real data from an experiment of rhythmic coordination in ensembles of interacting humans. The recurrence plots of topological portraits highlight collective transitions in coordination patterns that were elusive to more traditional methods. This sensitivity to collective transitions would be lost if the behavioral dynamics of individuals were treated as separate degrees of freedom instead of constituents of the topology that they collectively forge. Such multiscale topological portraits highlight collective aspects of coordination patterns that are irreducible to properties of individual parts. The present work demonstrates how the analysis of multiscale coordination dynamics can benefit from topological methods, thereby paving the way for further systematic quantification of complex, high-dimensional dynamics in living systems.

    View details for DOI 10.1016/j.jneumeth.2020.108672

    View details for PubMedID 32151601

  • Coordination Dynamics: A Foundation for Understanding Social Behavior. Frontiers in human neuroscience Tognoli, E., Zhang, M., Fuchs, A., Beetle, C., Kelso, J. A. 2020; 14: 317


    Humans' interactions with each other or with socially competent machines exhibit lawful coordination patterns at multiple levels of description. According to Coordination Dynamics, such laws specify the flow of coordination states produced by functional synergies of elements (e.g., cells, body parts, brain areas, people) that are temporarily organized as single, coherent units. These coordinative structures or synergies may be mathematically characterized as informationally coupled self-organizing dynamical systems (Coordination Dynamics). In this paper, we start from a simple foundation, an elemental model system for social interactions, whose behavior has been captured in the Haken-Kelso-Bunz (HKB) model. We follow a tried and tested scientific method that tightly interweaves experimental neurobehavioral studies and mathematical models. We use this method to further develop a body of empirical research that advances the theory toward more generalized forms. In concordance with this interdisciplinary spirit, the present paper is written both as an overview of relevant advances and as an introduction to its mathematical underpinnings. We demonstrate HKB's evolution in the context of social coordination along several directions, with its applicability growing to increasingly complex scenarios. In particular, we show that accommodating for symmetry breaking in intrinsic dynamics and coupling, multiscale generalization and adaptation are principal evolutions. We conclude that a general framework for social coordination dynamics is on the horizon, in which models support experiments with hypothesis generation and mechanistic insights.

    View details for DOI 10.3389/fnhum.2020.00317

    View details for PubMedID 32922277

  • Connecting empirical phenomena and theoretical models of biological coordination across scales. Journal of the Royal Society, Interface Zhang, M., Beetle, C., Kelso, J. A., Tognoli, E. 2019; 16 (157): 20190360


    Coordination in living systems-from cells to people-must be understood at multiple levels of description. Analyses and modelling of empirically observed patterns of biological coordination often focus either on ensemble-level statistics in large-scale systems with many components, or on detailed dynamics in small-scale systems with few components. The two approaches have proceeded largely independent of each other. To bridge this gap between levels and scales, we have recently conducted a human experiment of mid-scale social coordination specifically designed to reveal coordination at multiple levels (ensemble, subgroups and dyads) simultaneously. Based on this experiment, the present work shows that, surprisingly, a single system of equations captures key observations at all relevant levels. It also connects empirically validated models of large- and small-scale biological coordination-the Kuramoto and extended Haken-Kelso-Bunz (HKB) models-and the hallmark phenomena that each is known to capture. For example, it exhibits both multistability and metastability observed in small-scale empirical research (via the second-order coupling and symmetry breaking in extended HKB) and the growth of biological complexity as a function of scale (via the scalability of the Kuramoto model). Only by incorporating both of these features simultaneously can we reproduce the essential coordination behaviour observed in our experiment.

    View details for DOI 10.1098/rsif.2019.0360

    View details for PubMedID 31409241

  • Critical diversity: Divided or united states of social coordination PLOS ONE Zhang, M., Kelso, J., Tognoli, E. 2018; 13 (4): e0193843


    Much of our knowledge of coordination comes from studies of simple, dyadic systems or systems containing large numbers of components. The huge gap 'in between' is seldom addressed, empirically or theoretically. We introduce a new paradigm to study the coordination dynamics of such intermediate-sized ensembles with the goal of identifying key mechanisms of interaction. Rhythmic coordination was studied in ensembles of eight people, with differences in movement frequency ('diversity') manipulated within the ensemble. Quantitative change in diversity led to qualitative changes in coordination, a critical value separating régimes of integration and segregation between groups. Metastable and multifrequency coordination between participants enabled communication across segregated groups within the ensemble, without destroying overall order. These novel findings reveal key factors underlying coordination in ensemble sizes previously considered too complicated or 'messy' for systematic study and supply future theoretical/computational models with new empirical checkpoints.

    View details for DOI 10.1371/journal.pone.0193843

    View details for Web of Science ID 000429203800014

    View details for PubMedID 29617371

    View details for PubMedCentralID PMC5884498

  • On the Nature of Coordination in Nature Tognoli, E., Zhang, M., Kelso, J. : 375–382
  • The Human Dynamic Clamp: A Probe for Coordination Across Neural, Behavioral, and Social Scales Complexity and Synergetics Dumas, G., Lefebvre, A., Zhang, M., Tognoli, E., Kelso, J. Springer International Publishing. 2018: 317–332
  • Enhanced emotional responses during social coordination with a virtual partner INTERNATIONAL JOURNAL OF PSYCHOPHYSIOLOGY Zhang, M., Dumas, G., Kelso, J., Tognoli, E. 2016; 104: 33–43


    Emotion and motion, though seldom studied in tandem, are complementary aspects of social experience. This study investigates variations in emotional responses during movement coordination between a human and a Virtual Partner (VP), an agent whose virtual finger movements are driven by the Haken-Kelso-Bunz (HKB) equations of Coordination Dynamics. Twenty-one subjects were instructed to coordinate finger movements with the VP in either inphase or antiphase patterns. By adjusting model parameters, we manipulated the 'intention' of VP as cooperative or competitive with the human's instructed goal. Skin potential responses (SPR) were recorded to quantify the intensity of emotional response. At the end of each trial, subjects rated the VP's intention and whether they thought their partner was another human being or a machine. We found greater emotional responses when subjects reported that their partner was human and when coordination was stable. That emotional responses are strongly influenced by dynamic features of the VP's behavior, has implications for mental health, brain disorders and the design of socially cooperative machines.

    View details for DOI 10.1016/j.ijpsycho.2016.04.001

    View details for Web of Science ID 000379096400005

    View details for PubMedID 27094374

    View details for PubMedCentralID PMC4899205

  • Deterministic versus probabilistic causality in the brain: To cut or not to cut Comment on "Foundational perspectives on causality in large-scale brain networks" by M. Mannino and SL Bressler PHYSICS OF LIFE REVIEWS Zhang, M., Nordham, C., Kelso, J. 2015; 15: 136–38

    View details for DOI 10.1016/j.plrev.2015.10.002

    View details for Web of Science ID 000366440300028

    View details for PubMedID 26459061

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