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The situated HKB model: how sensorimotor spatial coupling can alter oscillatory brain dynamics.

Aguilera M, Bedia MG, Santos BA, Barandiaran XE - Front Comput Neurosci (2013)

Bottom Line: These results are compared with two different models: a decoupled HKB with no sensory input and a passively-coupled HKB that is also decoupled but receives a structured input generated by a situated agent.We also present the notion of neurodynamic signature as the dynamic pattern that correlates with a specific behavior and we show how only a situated agent can display this signature compared to an agent that simply receives the exact same sensory input.Finally, we discuss the limitations and possible generalization of our model to contemporary neuroscience and philosophy of mind.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Science and Engineering Systems, University of Zaragoza Zaragoza, Spain.

ABSTRACT
Despite the increase of both dynamic and embodied/situated approaches in cognitive science, there is still little research on how coordination dynamics under a closed sensorimotor loop might induce qualitatively different patterns of neural oscillations compared to those found in isolated systems. We take as a departure point the Haken-Kelso-Bunz (HKB) model, a generic model for dynamic coordination between two oscillatory components, which has proven useful for a vast range of applications in cognitive science and whose dynamical properties are well understood. In order to explore the properties of this model under closed sensorimotor conditions we present what we call the situated HKB model: a robotic model that performs a gradient climbing task and whose "brain" is modeled by the HKB equation. We solve the differential equations that define the agent-environment coupling for increasing values of the agent's sensitivity (sensor gain), finding different behavioral strategies. These results are compared with two different models: a decoupled HKB with no sensory input and a passively-coupled HKB that is also decoupled but receives a structured input generated by a situated agent. We can precisely quantify and qualitatively describe how the properties of the system, when studied in coupled conditions, radically change in a manner that cannot be deduced from the decoupled HKB models alone. We also present the notion of neurodynamic signature as the dynamic pattern that correlates with a specific behavior and we show how only a situated agent can display this signature compared to an agent that simply receives the exact same sensory input. To our knowledge, this is the first analytical solution of the HKB equation in a sensorimotor loop and qualitative and quantitative analytic comparison of spatially coupled vs. decoupled oscillatory controllers. Finally, we discuss the limitations and possible generalization of our model to contemporary neuroscience and philosophy of mind.

No MeSH data available.


Related in: MedlinePlus

Effects of fluctuations in the passively coupled system: (gray line) ξ(t), difference of the introduced fluctuations in φ(t) and φ*(t) and (black line) Δφ*(t), fluctuations in the difference between φ(t) and φ*(t) computed through Equation (5).
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Figure 9: Effects of fluctuations in the passively coupled system: (gray line) ξ(t), difference of the introduced fluctuations in φ(t) and φ*(t) and (black line) Δφ*(t), fluctuations in the difference between φ(t) and φ*(t) computed through Equation (5).

Mentions: As an example, we have simulated the situated HKB system with a passively-coupled HKB connected to it with an Euler step of 1 ms during a period of 5 s. We have introduced an additive white noise to the variables φ and φ* with a variance of 10−4. Then, ξ(t) will be equal to the difference between these two sources of noise, which will conserve their white noise structure with twice its variance (2·10−4) (Figure 9, gray line). With Equation (5) we can compute the resulting fluctuation Δφ*(t) that will determine the differences between the values of φ(t) and φ*(t) (Figure 9, black line). We can observe how the fluctuations in Δφ*(t) have lost the uncorrelated white noise structure of the initial fluctuation, and now have a radically different structure with different temporal correlations induced by the e−λ4t term. We can validate this result by comparing Δ φ*(t) computed with Equation (5) with the difference between φ(t) and φ*(t) measured experimentally without the effects reducing the system to a linear system around the attractor. That is, we can measure the error in the estimation of the fluctuation:e(t)=(φ(t)−φ*(t))−Δφ*(t)


The situated HKB model: how sensorimotor spatial coupling can alter oscillatory brain dynamics.

Aguilera M, Bedia MG, Santos BA, Barandiaran XE - Front Comput Neurosci (2013)

Effects of fluctuations in the passively coupled system: (gray line) ξ(t), difference of the introduced fluctuations in φ(t) and φ*(t) and (black line) Δφ*(t), fluctuations in the difference between φ(t) and φ*(t) computed through Equation (5).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3750630&req=5

Figure 9: Effects of fluctuations in the passively coupled system: (gray line) ξ(t), difference of the introduced fluctuations in φ(t) and φ*(t) and (black line) Δφ*(t), fluctuations in the difference between φ(t) and φ*(t) computed through Equation (5).
Mentions: As an example, we have simulated the situated HKB system with a passively-coupled HKB connected to it with an Euler step of 1 ms during a period of 5 s. We have introduced an additive white noise to the variables φ and φ* with a variance of 10−4. Then, ξ(t) will be equal to the difference between these two sources of noise, which will conserve their white noise structure with twice its variance (2·10−4) (Figure 9, gray line). With Equation (5) we can compute the resulting fluctuation Δφ*(t) that will determine the differences between the values of φ(t) and φ*(t) (Figure 9, black line). We can observe how the fluctuations in Δφ*(t) have lost the uncorrelated white noise structure of the initial fluctuation, and now have a radically different structure with different temporal correlations induced by the e−λ4t term. We can validate this result by comparing Δ φ*(t) computed with Equation (5) with the difference between φ(t) and φ*(t) measured experimentally without the effects reducing the system to a linear system around the attractor. That is, we can measure the error in the estimation of the fluctuation:e(t)=(φ(t)−φ*(t))−Δφ*(t)

Bottom Line: These results are compared with two different models: a decoupled HKB with no sensory input and a passively-coupled HKB that is also decoupled but receives a structured input generated by a situated agent.We also present the notion of neurodynamic signature as the dynamic pattern that correlates with a specific behavior and we show how only a situated agent can display this signature compared to an agent that simply receives the exact same sensory input.Finally, we discuss the limitations and possible generalization of our model to contemporary neuroscience and philosophy of mind.

View Article: PubMed Central - PubMed

Affiliation: Department of Computer Science and Engineering Systems, University of Zaragoza Zaragoza, Spain.

ABSTRACT
Despite the increase of both dynamic and embodied/situated approaches in cognitive science, there is still little research on how coordination dynamics under a closed sensorimotor loop might induce qualitatively different patterns of neural oscillations compared to those found in isolated systems. We take as a departure point the Haken-Kelso-Bunz (HKB) model, a generic model for dynamic coordination between two oscillatory components, which has proven useful for a vast range of applications in cognitive science and whose dynamical properties are well understood. In order to explore the properties of this model under closed sensorimotor conditions we present what we call the situated HKB model: a robotic model that performs a gradient climbing task and whose "brain" is modeled by the HKB equation. We solve the differential equations that define the agent-environment coupling for increasing values of the agent's sensitivity (sensor gain), finding different behavioral strategies. These results are compared with two different models: a decoupled HKB with no sensory input and a passively-coupled HKB that is also decoupled but receives a structured input generated by a situated agent. We can precisely quantify and qualitatively describe how the properties of the system, when studied in coupled conditions, radically change in a manner that cannot be deduced from the decoupled HKB models alone. We also present the notion of neurodynamic signature as the dynamic pattern that correlates with a specific behavior and we show how only a situated agent can display this signature compared to an agent that simply receives the exact same sensory input. To our knowledge, this is the first analytical solution of the HKB equation in a sensorimotor loop and qualitative and quantitative analytic comparison of spatially coupled vs. decoupled oscillatory controllers. Finally, we discuss the limitations and possible generalization of our model to contemporary neuroscience and philosophy of mind.

No MeSH data available.


Related in: MedlinePlus