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Data used for the purpose of machine learning are often erroneous. In this thesis, p-quasinorms (p<1) are employed as loss functions in order to increase the robustness of training algorithms for artificial neural networks. Numerical issues arising from these loss functions are addressed via enhanced optimization algorithms (proximal point methods; Frank-Wolfe methods) based on the (non-monotonic) Armijo-rule. Numerical experiments comprising 1100 test problems confirm the effectiveness of the approach. Depending on the parametrization, an average reduction of the absolute residuals of up to 64.6% is achieved (aggregated over 100 test problems).
In this thesis we study structure-preserving model reduction methods for the efficient and reliable approximation of dynamical systems. A major focus is the approximation of a nonlinear flow problem on networks, which can, e.g., be used to describe gas network systems. Our proposed approximation framework guarantees so-called port-Hamiltonian structure and is general enough to be realizable by projection-based model order reduction combined with complexity reduction. We divide the discussion of the flow problem into two parts, one concerned with the linear damped wave equation and the other one with the general nonlinear flow problem on networks.
The study around the linear damped wave equation relies on a Galerkin framework, which allows for convenient network generalizations. Notable contributions of this part are the profound analysis of the algebraic setting after space-discretization in relation to the infinite dimensional setting and its implications for model reduction. In particular, this includes the discussion of differential-algebraic structures associated to the network-character of our problem and the derivation of compatibility conditions related to fundamental physical properties. Amongst the different model reduction techniques, we consider the moment matching method to be a particularly well-suited choice in our framework.
The Galerkin framework is then appropriately extended to our general nonlinear flow problem. Crucial supplementary concepts are required for the analysis, such as the partial Legendre transform and a more careful discussion of the underlying energy-based modeling. The preservation of the port-Hamiltonian structure after the model-order- and complexity-reduction-step represents a major focus of this work. Similar as in the analysis of the model order reduction, compatibility conditions play a crucial role in the analysis of our complexity reduction, which relies on a quadrature-type ansatz. Furthermore, energy-stable time-discretization schemes are derived for our port-Hamiltonian approximations, as structure-preserving methods from literature are not applicable due to our rather unconventional parametrization of the solution.
Apart from the port-Hamiltonian approximation of the flow problem, another topic of this thesis is the derivation of a new extension of moment matching methods from linear systems to quadratic-bilinear systems. Most system-theoretic reduction methods for nonlinear systems rely on multivariate frequency representations. Our approach instead uses univariate frequency representations tailored towards user-defined families of inputs. Then moment matching corresponds to a one-dimensional interpolation problem rather than to a multi-dimensional interpolation as for the multivariate approaches, i.e., it involves fewer interpolation frequencies to be chosen. The notion of signal-generator-driven systems, variational expansions of the resulting autonomous systems as well as the derivation of convenient tensor-structured approximation conditions are the main ingredients of this part. Notably, our approach allows for the incorporation of general input relations in the state equations, not only affine-linear ones as in existing system-theoretic methods.
Structured Eurobonds - Optimal Construction, Impact on the Euro and the Influence of Interest Rates
(2020)
Structured Eurobonds are a prominent topic in the discussions how to complete the monetary and fiscal union. This work sheds light on several issues going hand in hand with the introduction of common bonds. At first a crucial question is on the optimal construction, e.g. what is the optimal common liability. Other questions that arise belong to the time after the introduction. The impact on several exchnage rates is examined in this work. Finally an approximation bias in forward-looking DSGE models is quantified which would lead to an adjustment of central bank interest rates and therefore has an impact on the other two topics.
The present thesis is devoted to a construction which defies generalisations about the prototypical English noun phrase (NP) to such an extent that it has been termed the Big Mess Construction (Berman 1974). As illustrated by the examples in (1) and (2), the NPs under study involve premodifying adjective phrases (APs) which precede the determiner (always realised in the form of the indefinite article a(n)) rather than following it.
(1) NoS had not been hijacked – that was too strong a word. (BNC: CHU 1766)
(2) He was prepared for a battle if the porter turned out to be as difficult a customer as his wife. (BNC: CJX 1755)
Previous research on the construction is largely limited to contributions from the realms of theoretical syntax and a number of cursory accounts in reference grammars. No comprehensive investigation of its realisations and uses has as yet been conducted. My thesis fills this gap by means of an exhaustive analysis of the construction on the basis of authentic language data retrieved from the British National Corpus (BNC). The corpus-based approach allows me to examine not only the possible but also the most typical uses of the construction. Moreover, while previous work has almost exclusively focused on the formal realisations of the construction, I investigate both its forms and functions.
It is demonstrated that, while the construction is remarkably flexible as concerns its possible realisations, its use is governed by probabilistic constraints. For example, some items occur much more frequently inside the degree item slot than others (as, too and so stand out for their particularly high frequency). Contrary to what is assumed in most previous descriptions, the slot is not restricted in its realisation to a fixed number of items. Rather than representing a specialised structure, the construction is furthermore shown to be distributed over a wide range of possible text types and syntactic functions. On the other hand, it is found to be much less typical of spontaneous conversation than of written language; Big Mess NPs further display a strong preference for the function of subject complement. Investigations of the internal structural complexity of the construction indicate that its obligatory components can optionally be enriched by a remarkably wide range of optional (if infrequent) elements. In an additional analysis of the realisations of the obligatory but lexically variable slots (head noun and head of AP), the construction is highlighted to represent a productive pattern. With the help of the methods of Collexeme Analysis (Stefanowitsch and Gries 2003) and Co-varying Collexeme Analysis (Gries and Stefanowitsch 2004b, Stefanowitsch and Gries 2005), the two slots are, however, revealed to be strongly associated with general nouns and ‘evaluative’ and ‘dimension’ adjectives, respectively. On the basis of an inspection of the most typical adjective-noun combinations, I identify the prototypical semantics of the Big Mess Construction.
The analyses of the constructional functions centre on two distinct functional areas. First, I investigate Bolinger’s (1972) hypothesis that the construction fulfils functions in line with the Principle of Rhythmic Alternation (e.g. Selkirk 1984: 11, Schlüter 2005). It is established that rhythmic preferences co-determine the use of the construction to some extent, but that they clearly do not suffice to explain the phenomenon under study. In a next step, the discourse-pragmatic functions of the construction are scrutinised. Big Mess NPs are demonstrated to perform distinct information-structural functions in that the non-canonical position of the AP serves to highlight focal information (compare De Mönnink 2000: 134-35). Additionally, the construction is shown to place emphasis on acts of evaluation. I conclude the construction to represent a contrastive focus construction.
My investigations of the formal and functional characteristics of Big Mess NPs each include analyses which compare individual versions of the construction to one another (e.g. the As Big a Mess, Too Big a Mess and So Big a Mess Constructions). It is revealed that the versions are united by a shared core of properties while differing from one another at more abstract levels of description. The question of the status of the constructional versions as separate constructions further receives special emphasis as part of a discussion in which I integrate my results into the framework of usage-based Construction Grammar (e.g. Goldberg 1995, 2006).
The dissertation includes three published articles on which the development of a theoretical model of motivational and self-regulatory determinants of the intention to comprehensively search for health information is based. The first article focuses on building a solid theoretical foundation as to the nature of a comprehensive search for health information and enabling its integration into a broader conceptual framework. Based on subjective source perceptions, a taxonomy of health information sources was developed. The aim of this taxonomy was to identify most fundamental source characteristics to provide a point of reference when it comes to relating to the target objects of a comprehensive search. Three basic source characteristics were identified: expertise, interaction and accessibility. The second article reports on the development and evaluation of an instrument measuring the goals individuals have when seeking health information: the ‘Goals Associated with Health Information Seeking’ (GAINS) questionnaire. Two goal categories (coping focus and regulatory focus) were theoretically derived, based on which four goals (understanding, action planning, hope and reassurance) were classified. The final version of the questionnaire comprised four scales representing the goals, with four items per scale (sixteen items in total). The psychometric properties of the GAINS were analyzed in three independent samples, and the questionnaire was found to be reliable and sufficiently valid as well as suitable for a patient sample. It was concluded that the GAINS makes it possible to evaluate goals of health information seeking (HIS) which are likely to inform the intention building on how to organize the search for health information. The third article describes the final development and a first empirical evaluation of a model of motivational and self-regulatory determinants of an intentionally comprehensive search for health information. Based on the insights and implications of the previous two articles and an additional rigorous theoretical investigation, the model included approach and avoidance motivation, emotion regulation, HIS self-efficacy, problem and emotion focused coping goals and the intention to seek comprehensively (as outcome variable). The model was analyzed via structural equation modeling in a sample of university students. Model fit was good and hypotheses with regard to specific direct and indirect effects were confirmed. Last, the findings of all three articles are synthesized, the final model is presented and discussed with regard to its strengths and weaknesses, and implications for further research are determined.
In dem Gebiet der Informationsextraktion angesiedelt kombiniert diese Arbeit mehrere Verfahren aus dem Bereich des maschinellen Lernens. Sie stellt einen neuen Algorithmus vor, der teil-überwachtes Lernen mit aktivem Lernen verknüpft. Ausgangsbasis ist die Analyse der Daten, indem sie in mehrere Sichten aufgeteilt werden. Hier werden die Eingaben verschiedener Personen unterteilt. Jeweils getrennt voneinander erzeugt der Algorithmus mittels Klassifizierern Modelle, die aus den individuellen Auszeichnungen der Personen aufgebaut werden. Um die dafür benötigte Datenmenge zu erhalten wird Crowdsourcing genutzt, dass es ermöglicht eine große Anzahl an Personen zu erreichen. Die Personen erhalten die Aufgabe, Texte zu annotieren. Einerseits wird dies initial für einen historischen Textkorpus vorgenommen. Dabei wird aufgeführt, welche Schritte notwendig sind, um die Annotationsaufgabe in Crowdsourcing-Portalen zur Bearbeitung anzubieten und durchzuführen. Andererseits wird ein aktueller Datensatz von Kurznachrichten genutzt. Der Algorithmus wird auf diese Beispieldatensätze angewandt. Durch Experimente wird die Ermittlung der optimalen Parameterauswahl durchgeführt. Außerdem werden die Ergebnisse mit den Resultaten bisheriger Algorithmen verglichen.
Internet interventions have gained popularity and the idea is to use them to increase the availability of psychological treatment. Research suggests that internet interventions are effective for a number of psychological disorders with effect sizes comparable to those found in face-to-face treatment. However, when provided as an add-on to treatment as usual, internet interventions do not seem to provide additional benefit. Furthermore, adherence and dropout rates vary greatly between studies, limiting the generalizability of the findings. This underlines the need to further investigate differences between internet interventions, participating patients, and their usage of interventions. A stronger focus on the processes of change seems necessary to better understand the varying findings regarding outcome, adherence and dropout in internet interventions. Thus, the aim of this dissertation was to investigate change processes in internet interventions and the factors that impact treatment response. This could help to identify important variables that should be considered in research on internet interventions as well as in clinical settings that make use of internet interventions.
Study I (Chapter 5) investigated early change patterns in participants of an internet intervention targeting depression. Data from 409 participants were analyzed using Growth Mixture Modeling. Specifically a piecewise model was applied to model change from screening to registration (pretreatment) and early change (registration to week four of treatment). Three early change patterns were identified; two were characterized by improvement and one by deterioration. The patterns were predictive of treatment outcome. The results therefore indicated that early change should be closely monitored in internet interventions, as early change may be an important indicator of treatment outcome.
Study II (Chapter 6) picked up on the idea of analyzing change patterns in internet interventions and extended it by using the Muthen-Roy model to identify change-dropout patterns. A sligthly bigger sample of the dataset from Study I was analyzed (N = 483). Four change-dropout patterns emerged; high risk of dropout was associated with rapid improvement and deterioration. These findings indicate that clinicians should consider how dropout may depend on patient characteristics as well as symptom change, as dropout is associated with both deterioration and a good enough dosage of treatment.
Study III (Chapter 7) compared adherence and outcome in different participant groups and investigated the impact of adherence to treatment components on treatment outcome in an internet intervention targeting anxiety symptoms. 50 outpatient participants waiting for face- to-face treatment and 37 self-referred participants were compared regarding adherence to treatment components and outcome. In addition, outpatient participants were compared to a matched sample of outpatients, who had no access to the internet intervention during the waiting period. Adherence to treatment components was investigated as a predictor of treatment outcome. Results suggested that especially adherence may vary depending on participant group. Also using specific measures of adherence such as adherence to treatment components may be crucial to detect change mechanisms in internet interventions. Fostering adherence to treatment components in participants may increase the effectiveness of internet interventions.
Results of the three studies are discussed and general conclusions are drawn.
Implications for future research as well as their utility for clinical practice and decision- making are presented.