The role of long-term power-law memory in controlling large-scale dynamical networks.

Controlling large-scale dynamical networks is crucial to understand and, ultimately, craft the evolution of complex behavior. While broadly speaking we understand how to control Markov dynamical networks, where the current state is only a function of its previous state, we lack a general understanding of how to control dynamical networks whose current state depends on states in the distant past (i.e. long-term memory). Therefore, we require a different way to analyze and control the more prevalent long-term memory dynamical networks. Herein, we propose a new approach to control dynamical networks exhibiting long-term power-law memory dependencies. Our newly proposed method enables us to find the minimum number of driven nodes (i.e. the state vertices in the network that are connected to one and only one input) and their placement to control a long-term power-law memory dynamical network given a specific time-horizon, which we define as the 'time-to-control'. Remarkably, we provide evidence that long-term power-law memory dynamical networks require considerably fewer driven nodes to steer the network's state to a desired goal for any given time-to-control as compared with Markov dynamical networks. Finally, our method can be used as a tool to determine the existence of long-term memory dynamics in networks.

Sampling-Based Nonlinear Stochastic Optimal Control for Neuromechanical Systems.

Determining how the nervous system controls tendon-driven bodies remains an open question. Stochastic optimal control (SOC) has been proposed as a plausible analogy in the neuroscience community. SOC relies on solving the Hamilton-Jacobi-Bellman equation, which seeks to minimize a desired cost function for a given task with noisy controls. We evaluate and compare three SOC methodologies to produce tapping by a simulated planar 3-joint human index finger: iterative Linear Quadratic Gaussian (iLQG), Model-Predictive Path Integral Control (MPPI), and Deep Forward-Backward Stochastic Differential Equations (FBSDE). We show that averaged over 128 repeats these methodologies can place the fingertip at the desired final joint angles but-because of kinematic redundancy and the presence of noise-they each have joint trajectories and final postures with different means and variances. iLQG in particular, had the largest kinematic variance and departure from the final desired joint angles. We demonstrate that MPPI and FBSDE have superior performance for such nonlinear, tendon-driven systems with noisy controls.Clinical relevance- The mathematical framework provided by MPPI and FBSDE may be best suited for tendon-driven anthropomorphic robots, exoskeletons, and prostheses for amputees.

Neighborhood Characteristics: Influences on Pain and Physical Function in Youth at Risk for Chronic Pain.

Neighborhood features such as community socioeconomic status, recreational facilities, and parks have been correlated to the health outcomes of the residents living within those neighborhoods, especially with regard to health-related quality of life, body mass index, and physical activity. The interplay between one's built environment and one's perceptions may affect physical health, well-being, and pain experiences. In the current study, neighborhood characteristics and attitudes about physical activity were examined in a high-risk (youths with a parent with chronic pain) and low-risk (youths without a parent with chronic pain) adolescent sample. There were significant differences in neighborhood characteristics between the high-risk (n = 62) and low-risk (n = 77) samples (ages 11-15), with low-risk participants living in residences with more walkability, closer proximity to parks, and higher proportion of neighborhood residents having college degrees. Results indicate that neighborhood features (e.g., walkability and proximity to parks), as well as positive attitudes about physical activity were correlated with lower levels of pain and pain-related disability, and higher performance in physical functioning tests. These findings suggest that the built environment may contribute to pain outcomes in youth, above and beyond the influence of family history of pain.