Institut für Wirtschaftsinformatik (IIS)
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In past digital health interventions, an issue has been that participants drop out over time which is referred to as the ”law of attrition” (Eysenbach, 2005). Based on this, we propose that though initially, participants respond to the intervention, there is a hypothesized second diminishing e↵ect of an intervention. However, we suggest that on top, there is a third e↵ect. Independent of the individual notification or nudge, people could build the knowledge, skills and practice needed to independently engage in the behavior themselves (schraefel and Hekler, 2020). Using behavioral theory and inspired by prior animal computational models of behavior, we propose a dynamical computational model to allow for a separation of intervention and internalization. It is targeted towards the specific case of the HeartSteps intervention that could not explain a diminishing immediate effect of the intervention, second hypothesized e↵ect, while a person’s overall steps remained constant, third e↵ect (Klasnja et al., 2019). We incorporate a habituation mechanism from learning theory that can account for the immediate diminishing e↵ect. At the same time, a reinforcement mechanism allows participants to internalize the message and engage in behavior independently. The simulation shows the importance of a participant’s responsiveness to the intervention and a sufficient recovery period after each notification. To estimate the model, we use data from the HeartSteps intervention (Klasnja et al., 2019; Liao et al., 2020), a just-in-time adaptive intervention that sent two to five walking suggestions per day. We run a Bayesian estimation with Stan in R. Additional validation tests are needed to estimate the accuracy of the model for di↵erent individuals. It could however serve as a template for future just-intime adaptive interventions due to its generic structure. In addition, this model is of high practical relevance as its derived dynamics can be used to improve future walking suggestions and ultimately optimize notification-based digital health interventions.
The computational analysis and the optimization of transport and mixing processes in fluid flows are of ongoing scientific interest. Transfer operator methods are powerful tools for the study of these processes in dynamical systems. The focus in this context has been mostly on closed dynamical systems and the main applications have been geophysical flows.
In this thesis, we consider transport and mixing in closed flow systems and in open flow systems that mimic technical mixing devices. Via transfer operator methods, we study the coherent behavior in closed example systems including a turbulent Rayleigh-Bénard convection flow and consider the finite-time mixing of two fluids. We extend the transfer operator framework to specific open flows. In particular, we study time-periodic open flow systems with constant inflow and outflow of fluid particles and consider several example systems. In this case, the transfer operator is represented by a transition matrix of a time-homogeneous absorbing Markov chain restricted to finite transient states. The chaotic saddle and its stable and unstable manifolds organize the transport processes in open systems. We extract these structures directly from leading eigenvectors of the transition matrix. For a constant source of two fluids in different colors, the mass distribution in the mixer and its outlet region converges to an invariant mixing pattern. In parameter studies, we quantify the degree of mixing of the resulting patterns by several mixing measures. More recently, network-based methods that construct graphs on trajectories of fluid particles have been developed to study coherent behavior in fluid flow. We use a method based on diffusion maps to extract organizing structures in open example systems directly from trajectories of fluid particles and extend this method to describe the mixing of two types of fluids.
