A dynamical systems view of motor preparation

To gain insights about dynamic networks, the dominant paradigm is to study discrete snapshots , or timeslices , as the interactions evolve. Here, we develop and test a new mathematical framework where network evolution is handled over continuous time, giving an elegant dynamical systems representation for the important concept of node centrality. The resulting system allows us to track the relative influence of each individual. This new setting is natural in many digital applications, offering both conceptual and computational advantages. The novel differential equations approach is convenient for modelling and analysis of network evolution and gives rise to an interesting application of the matrix logarithm function. From a computational perspective, it avoids the awkward up-front compromises between accuracy, efficiency and redundancy required in the prevalent discrete-time setting. Instead, we can rely on state-of-the-art ODE software, where discretization takes place adaptively in response to the prevailing system dynamics. The new centrality system generalizes the widely used Katz measure, and allows us to identify and track, at any resolution, the most influential nodes in terms of broadcasting and receiving information through time-dependent links. In addition to the classical static network notion of attenuation across edges, the new ODE also allows for attenuation over time, as information becomes stale. This allows ‘running measures’ to be computed, so that networks can be monitored in real time over arbitrarily long intervals. With regard to computational efficiency, we explain why it is cheaper to track good receivers of information than good broadcasters. An important consequence is that the overall broadcast activity in the network can also be monitored efficiently. We use two synthetic examples to validate the relevance of the new measures. We then illustrate the ideas on a large-scale voice call network, where key features are discovered that are not evident from snapshots or aggregates.

Download Full-text

On the local interpretation of Takagi-Sugeno fuzzy models from a dynamical systems view

Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301) ◽

10.1109/acc.2002.1024859 ◽

2003 ◽

Author(s):

Seok-beom Lee ◽

G.G. Yen

Keyword(s):

Dynamical Systems ◽

Fuzzy Models ◽

Takagi Sugeno ◽

Systems View

Download Full-text

Rise-to-threshold and dynamical systems views of proactive inhibition

10.1101/2021.01.16.426928 ◽

2021 ◽

Author(s):

Vishal Rawji ◽

Sachin Modi ◽

Lorenzo Rocchi ◽

Marjan Jahanshahi ◽

John C. Rothwell

Keyword(s):

Dynamical Systems ◽

Motor Cortex ◽

Pulse Width ◽

Threshold Model ◽

Motor Preparation ◽

Proactive Inhibition ◽

Movement Execution ◽

Systems Perspective ◽

Systems Models ◽

Dynamical Systems Models

AbstractSuccessful models of movement should encompass the flexibility of the human motor system to execute movements under different contexts. One such context-dependent modulation is proactive inhibition, a type of behavioural inhibition concerned with responding with restraint. Whilst movement has classically been modelled as a rise-to-threshold process, there exists a lack of empirical evidence for this in limb movements. Alternatively, the dynamical systems view conceptualises activity during motor preparation as setting the initial state of a dynamical system, that evolves into the movement upon receipt of a trigger. We tested these models by measuring how proactive inhibition influenced movement preparation and execution in humans. We changed the orientation (PA: postero-anterior and AP: antero-posterior flowing currents) and pulse width (120 μs and 30 μs) of motor cortex transcranial magnetic stimulation to probe different corticospinal interneuron circuits. PA and AP interneuron circuits represent the dimensions of a state space upon which motor cortex activity unfolds during motor preparation and execution. AP30 inputs were inhibited at the go cue, regardless of proactive inhibition, whereas PA120 inputs scaled inversely with the probability of successful inhibition. When viewed through a rise-to-threshold model, proactive inhibition was implemented by delaying the trigger to move, suggesting that motor preparation and execution are independent. A dynamical systems perspective showed that proactive inhibition was marked by a shift in the distribution of interneuron networks (trajectories) during movement execution, despite normalisation for reaction time. Viewing data through the rise-to-threshold and dynamical systems models reveal complimentary mechanisms by which proactive inhibition is implemented.Key pointsWe view proactive inhibition through the rise-to-threshold and dynamical systems models.We change the orientation (PA: postero-anterior and AP: antero-posterior flowing currents) and pulse width (120 μs and 30 μs) of transcranial magnetic stimulation to probe interneuron networks in motor cortex during behavioural tasks employing proactive inhibition.When viewed through a rise-to-threshold model, proactive inhibition was implemented by delaying the trigger to move, suggesting that motor preparation and execution are independent.A dynamical systems perspective showed that despite normalisation for reaction time, the trajectory/balance between PA120 and AP30 interneuron inputs during movement execution depended on proactive inhibition.Viewing data through the rise-to-threshold and dynamical systems models reveal complimentary mechanisms by which proactive inhibition is implemented.

Download Full-text