J. A. S. KELSO1,2, G. DUMAS1, E. TOGNOLI1, G. C. DE GUZMAN1

Bridging neural , behavioral and socia l coordinat ion dynamics using the human dynamic c lamp1. Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton, FL2. Intelligent System Research Centre, University of Ulster, Derry, N. Ireland

Introduction Take-home messages

Supports

References

Contact uswww.ccs.fau.edu/hbbl/kelso@ccs.fau.edu

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Kelso, J. A. S., de Guzman, G. C., Reveley, C., & Tognoli, E. (2009). Virtual Partner Interaction (VPI): Exploring Novel Behaviors via Coordination Dynamics. PLoS ONE, 4(6), e5749. doi:10.1371/journal.pone.0005749.t002

Jirsa, V. K., & Kelso, J. A. S. (2005). The excitator as a minimal model for the coordination dynamics of discrete and rhythmic movement generation. Journal of motor behavior, 37(1), 35–51. doi:10.3200/JMBR.37.1.35-51

Righetti, L., Buchli, J., & Ijspeert, A. J. (2009). Adaptive frequency oscillators and applications. The Open Cybernetics and Systemics Journal, 3, 64–69.

Schöner, G., & Kelso, J. A. S. (1988). A dynamic pattern theory of behavioral change. Journal of Theoretical Biology, 135(4), 501–524.

- The human dynamic clamp allows real-time interaction between a human and empirically grounded theoretical models of behavior; - The general paradigm allows one to test principle-based models by exploring their entire parameter space; - The Virtual Partner (VP) behavioral repertoire can be extended to dif.ferent task settings (rhythmic, discrete, adaptive and intentional coordination) and modalities (e.g. eye movements, vocalization, sweat glands, EEG, etc. ); - Novel behavioral patterns can be validated by simulations; - The Virtual Teacher (VT) opens up new venues for rehabilitation and learning.

The human dynamic clamp provides a novel integrative paradigm for the multidisciplinary study of human brain and behavior, with theory and experiment working hand in hand. The bottom line is that as long as one has a decent model of behavior, broadly def.ined at dif.ferent levels for dif.ferent functions, and as long as there is a vehicle for two-way interaction, then the conditions are created for a deeper understanding of both the model and what the model is purported to be of.

Previous research used the HKB model of behavioral coordination (Figure 1) and uncovered behaviors never observed before in social interactions, including an ability to elicit the attribution of intention to the VP. Here we describe three additional theoretical models expanding the VP repertoire across rhythmic, discrete, adaptive, and directed behaviors. This illustrates how the human dynamic clamp paradigm can be generalized across dif.ferent tasks and opens up new possibilities for the development of “social computational neuroscience”.

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i Adaptive BehaviorParameter dynamics and frequency coordination.v Discrete and Rhythmic Behavior

Multiple modes of coordination from the same dynamics:The Jirsa-Kelso (2005) Excitator model.

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Directed BehaviorIntentional coupling and symmetry breaking.z

The Jirsa-Kelso (2005) Excitator model def.ines a universal class of two-dimensional dynamical systems and is able to exhibit both rhythmic and discrete movements. Moreover, it connects directly to known neurobiological models (e.g. Fitzhugh-Nagumo). The Excitator exhibits three types of dynamics and changes between them depending on parameters (Figure 2).

Equations read as follow:

where

Embedding the Excitator into the VP allows study of interaction with humans for both discrete and rhythmic behaviors, including transitions. This demonstrates how a unique model can expand the VP behavioral repertoire while keeping a coherent dynamical perspective.

Any parameter can be turned into a variable for modeling human adaptive behavior. Frequency of movement provides an ideal example. Both the HKB and the Excitator adapt their frequency with the addition of a new dif.ferential equation.

Following Righetti and colleagues (2009): where f and F(t) terms stand for intrinsic and coupling dynamics.

Behavior is often directedtoward a specif.ic goal, e.g. a specif.ic phase relationship.

Such directed behavior may be mirrored in the attractor landscape forming a dif.ferential equation governing the relative phase dynamics (Schöner and Kelso, 1988):

Here the VP requires an intended relative phase ψ. When ψ is equal to π/2, this breaks the symmetry of the coupling. The VP becomes a VT, a Virtual Teacher.

Figure 2: The Excitator as a VP in the Human Dynamic Clamp. (A, C, E) Time series of reciprocal interaction between a human (in red) and virtual partner, The Excitator (in blue). (B,D,F) Related phase space, null-clines and phase flows.

(A,B) Monostable regime: Participant makes discrete movements and returns to rest. Parameters of the VP: a=1.3;b=1;A=0.1;B=0.25;τ=0.1; ω=1.5. (C,D) Bistable regime: Participant switches discretely between two positions. Parameters of the VP: a=0;b=2.3;A=0.1;B=0.25;τ=0.1; ω=1.5. (E,F) Limit cycle regime: Participant moves continuously at a fixed frequency. Parameters of the VP: a=0;b=0.5;A=1.5;B=-0.1;τ=1; ω=1.5.

Figure 3: (a) Example of interaction between an Excitator as a VP (blue) adapting its pace to a human participant (red). (b) Dynamics of the internal frequency parameter (ω) of the VP (blue) compared to the dynamics of the particpant’s frequency (red). Parameters of the VP model: a=0;b=0;A=1;B=-0.2τ=1; ω=1;K=1.

Figure 4: (a) Example of interaction between a human (in red) and a virtual partner (in blue) embedding the Schoner-Kelso (1988) model of intentional coordination for an intended relative phase of π/2. Dashed line indicates when the VP returns to the HKB equation. We can observe the remaining effect on the human who keeps a slight delay compared to the VP. Parameters of the VP model: a=0.641;b=0.00709;A=0.12;B=0.025;C=1;ω=1; ψ=π/2. (b) Color wheel indicates the intended relative phase ψ. Relative phase evolutions in time for random initial conditions and different intended related phases ψ.

Figure 5: The Human Dynamic Clamp as a bridge between Experiments and Models.

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Virtual Teacher Interaction (VTI)

Excitator in Monostable Régime: RAPID BALLISTIC MOVEMENTS

Excitator in Bistable Régime: DISCRETE MOVEMENTS FROM ONE STATE TO ANOTHER

Excitator in Limit Cycle Régime: CONTINUOUS RHYTHMIC MOVEMENTS

Figure 1: a) Schematic of the HDC system. Human coordinates finger movement with a virtual partner (VP) displayed on a screen. Human's motion (position, velocity) is digitized and fed into a computer, where a software program computes in real time the corresponding position of the VP following the HKB model of coordination dynamics. b) Timeseries of interaction between VP (blue) and a human (orange). VP’s goal is anti-phase and human’s goal is in-phase. Note the in-phase to anti-phase transitions. .

We propose a general paradigm called the "human dynamic clamp" consisting of a human interacting reciprocally with a virtual partner (VP) (Kelso, et al., 2009). Akin to the dynamic clamp of cellular neuroscience, both the intrinsic dynamics of the VP and its coupling to the human can be manipulated in real-time thereby enabling a fully parametric exploration of the relationship between humans and human surrogates in a variety of task settings.

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HKB with an intended relative phase HKB without any intended relative phase