Working with the Kids at Home? Tips from an Experienced Parent

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Chapter 2: Time Series

Time series is “simply a list of numbers assumed to measure some process sequentially in time” (Stergiou et al. 2004). Mathematicians have a more formal definition, that is, a set or a sequence of observations, with each one recorded at specific times, or at least sequentially (Brockwell and Davis 2002; Box et al. 2008). Time series are created from multiple sources for research purposes to understand various behaviors. For example, social scientists could collect graduation rates, physiologists record heart rates, economists study consumer spending, and climatologists examine weather patterns. Basically, any time observations are taken repeatedly over time, from any source or behavior, a time series is created

Chapter 5: Surrogation

One of the goals of time series analysis is to understand the underlying mechanisms that generate different dynamics for different time series. If a time series is not a product of random process, then we can assume that some kind of dynamics govern the time series. The question is what kinds of dynamics are controlling the time series. For nonlinear time series analysis, our focus is on nonlinear dynamics, and one of the goals is to characterize those dynamics by applying nonlinear tools. However, it is important to establish evidence of nonlinearity in a time series first in order to avoid obtaining possible spurious results by applying nonlinear tools to the system that does not contain nonlinearity. Second, nonlinearity is considered as one of the key features of time series that exhibit chaos, which has been shown to have a potential link with overall health of the biological system (Amato 1992; Buchman et al. 2001; Cavanaugh et al. 2010; Garfinkel et al. 1992; Goldstein et al. 1998; Orsucci 2006; Slutzky et al. 2001; Toweill and Goldstein 1998; Wagner et al. 1996). Therefore, in terms of detecting chaos in a time series, identifying the presence of nonlinearity in the system is essential

Grant funding strategy: Which grants to apply for?

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Choosing What to Do or Not to Do on the Job

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A robust technique for optimal fitting of roll-over shapes of human locomotor systems

The roll-over shape (ROS) effectively characterizes the lower limb\u27s ability to roll forward during the single-limb support phase of human walking. ROS is modelled as an optimally fitted circular arc to the center of pressure (CoP) data transformed in the shank/leg-based local coordinate system. The commonly used method for optimal fitting of ROS is complex to implement and eliminates inherent individual variability in the ROS parameters during walking. We propose and validate a novel computerized method for optimal fitting of roll-over shapes of the lower limb during walking. Gait data of a healthy individual from Winter\u27s book was used to generate ankle-foot and knee-ankle-foot roll-over shapes using the proposed method. The goodness of fit and form of both the roll-over shapes were validated with the literature. To test the robustness of the proposed technique, small random perturbations were introduced to the transformed CoP data and the effect of these small changes in the data on the ROS parameters was studied. The ROS parameters such as radius, arc length, subtended arc angle, and horizontal and vertical shift in the arc center did not change substantially with small changes in the CoP data. The proposed method is computationally efficient, and easy to implement for optimal fitting and characterization of ROS

Individuals with Peripheral Artery Disease Alter Spatiotemporal Gait Parameters When Walking With Pain versus Without Pain

This abstract compares the spatiotemporal walking parameters of individuals with peripheral artery disease at the time they first begin walking, the time when they first feel pain, and the time when they can no longer continue walking

Transtibial Amputee Joint Motion has Increased Attractor Divergence During Walking Compared to Non-Amputee Gait

The amputation and subsequent prosthetic rehabilitation of a lower leg affects gait. Dynamical systems theory would predict the use of a prosthetic device should alter the functional attractor dynamics to which the system self-organizes. Therefore, the purpose of this study was to compare the largest Lyapunov exponent (a nonlinear tool for assessing attractor dynamics) for amputee gait compared to healthy non-amputee individuals. Fourteen unilateral, transtibial amputees and fourteen healthy, non-amputee individuals ambulated on a treadmill at preferred, self-selected walking speed. Our results showed that the sound hip (p = 0.013), sound knee (p = 0.05), and prosthetic ankle (p = 0.023) have significantly greater largest Lyapunov exponents than healthy non-amputees. Furthermore, the prosthetic ankle has a significantly greater (p = 0.0.17) largest Lyapunov exponent than the sound leg ankle. These findings indicate attractor states for amputee gait with increased divergence. The increased attractor divergence seems to coincide with decreased ability for motor control between the natural rhythms of the individual and those of the prosthetic device. Future work should consider the impact of different prostheses and rehabilitation on the attractor dynamics

Amputation effects on the underlying complexity within transtibial amputee ankle motion

The presence of chaos in walking is considered to provide a stable, yet adaptable means for locomotion. This study examined whether lower limb amputation and subsequent prosthetic rehabilitation resulted in a loss of complexity in amputee gait. Twenty-eight individuals with transtibial amputation participated in a 6 week, randomized cross-over design study in which they underwent a 3 week adaptation period to two separate prostheses. One prosthesis was deemed “more appropriate” and the other “less appropriate” based on matching/mismatching activity levels of the person and the prosthesis. Subjects performed a treadmill walking trial at self-selected walking speed at multiple points of the adaptation period, while kinematics of the ankle were recorded. Bilateral sagittal plane ankle motion was analyzed for underlying complexity through the pseudoperiodic surrogation analysis technique. Results revealed the presence of underlying deterministic structure in both prostheses and both the prosthetic and sound leg ankle (discriminant measure largest Lyapunov exponent). Results also revealed that the prosthetic ankle may be more likely to suffer loss of complexity than the sound ankle, and a “more appropriate” prosthesis may be better suited to help restore a healthy complexity of movement within the prosthetic ankle motion compared to a “less appropriate” prosthesis (discriminant measure sample entropy). Results from sample entropy results are less likely to be affected by the intracycle periodic dynamics as compared to the largest Lyapunov exponent. Adaptation does not seem to influence complexity in the system for experienced prosthesis users