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- Institut für Wirtschaftsinformatik (IIS) (3) (entfernen)
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, the authors consider transport and mixing in closed flow systems and in open flow systems that mimic technical mixing devices. Via transfer operator methods, They study the coherent behavior in closed example systems including a turbulent Rayleigh-Bénard convection flow and consider the finite-time mixing of two fluids. They extend the transfer operator framework to specific open flows. In particular, they 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. The authors 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, they 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. They 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.
Mental health is an important factor in an individuals' life. Online-based interventions have been developed for the treatment of various mental disorders. During these interventions, a large amount of patient-specific data is gathered that can be utilized to increase treatment outcomes by informing decision-making processes of psychotherapists, experts in the field, and patients. The articles included in this dissertation focus on the analysis of such data collected in digital psychological treatments by using machine learning approaches. This dissertation utilizes various machine learning methods such as Bayesian models, regularization techniques, or decision trees to predict different psychological factors, such as mood or self-esteem, dropout of patients, or treatment outcomes and costs. These models are evaluated using a variety of performance metrics, for example, receiver operating characteristics curve, root mean square error, or specialized performance metrics for Bayesian inference. These types of analyses can support decision- making for psychologists and patients, which can, in turn, lead to better recommendations and subsequently to increased outcomes for patients and simultaneously more insight about the interplay between psychological factors. The analysis of user journey data has not yet been fully examined in the field of psychological research. A process for this endeavor is developed and a technical implementation is provided for the research community. The application of machine learning in this context is still in its infancy. Thus, another contribution is the exploration and application of machine learning techniques for the revelation of correlations between psychological factors or characteristics and treatment outcomes as well as their prediction. Additionally, economic factors are predicted to develop a process for treatment type recommendations. This approach can be utilized for finding the optimal treatment type for patients on an individual level considering predicted treatment outcomes and costs. By evaluating the predictive accuracy of multiple machine learning techniques based on various performance metrics, the importance of considering heterogeneity among patients' behavior and affect is highlighted in some articles. Furthermore, the potential of machine learning-based decision support systems in clinical practice has been examined from a psychotherapists' point of view.
Technological development made it possible to store and process data on a scale not imaginable decades ago — a development that also includes network data. A particular characteristic of network data is that, unlike standard data, the objects of interest, called nodes, have relationships to (possibly all) other objects in the network. Collecting empirical data is often complicated and cumbersome, hence, the observed data are typically incomplete and might also contain other types of errors. Because of the interdependent structure of network data, these errors have a severe impact on network analysis methods. This cumulative dissertation is about the impact of erroneous network data on centrality measures, which are methods to assess the position of an object, for example a person, with respect to all other objects in a network. Existing studies have shown that even small errors can substantially alter these positions. The impact of errors on centrality measures is typically quantified using a concept called robustness. The articles included in this dissertation contribute to a better understanding of the robustness of centrality measures in several aspects. It is argued why the robustness needs to be estimated and a new method is proposed. This method allows researchers to estimate the robustness of a centrality measure in a specific network and can be used as a basis for decision making. The relationship between network properties and the robustness of centrality measures is analyzed. Experimental and analytical approaches show that centrality measures are often more robust in networks with a larger average degree. The study of the impact of non-random errors on the robustness suggests that centrality measures are often more robust if missing nodes are more likely to belong to the same community compared to missingness completely at random. For the development of imputation procedures based on machine learning techniques, a process for the evaluation of node embedding methods is proposed.