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Institut
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For decades, academics and practitioners aim to understand whether and how (economic) events affect firm value. Optimally, these events occur exogenously, i.e. suddenly and unexpectedly, so that an accurate evaluation of the effects on firm value can be conducted. However, recent studies show that even the evaluation of exogenous events is often prone to many challenges that can lead to diverse interpretations, resulting in heated debates. Recently, there have been intense debates in particular on the impact of takeover defenses and of Covid-19 on firm value. The announcements of takeover defenses and the propagation of Covid-19 are exogenous events that occur worldwide and are economically important, but have been insufficiently examined. By answering open research questions, this dissertation aims to provide a greater understanding about the heterogeneous effects that exogenous events such as the announcements of takeover defenses and the propagation of Covid-19 have on firm value. In addition, this dissertation analyzes the influence of certain firm characteristics on the effects of these two exogenous events and identifies influencing factors that explain contradictory results in the existing literature and thus can reconcile different views.
In common shape optimization routines, deformations of the computational mesh
usually suffer from decrease of mesh quality or even destruction of the mesh.
To mitigate this, we propose a theoretical framework using so-called pre-shape
spaces. This gives an opportunity for a unified theory of shape optimization, and of
problems related to parameterization and mesh quality. With this, we stay in the
free-form approach of shape optimization, in contrast to parameterized approaches
that limit possible shapes. The concept of pre-shape derivatives is defined, and
according structure and calculus theorems are derived, which generalize classical
shape optimization and its calculus. Tangential and normal directions are featured
in pre-shape derivatives, in contrast to classical shape derivatives featuring only
normal directions on shapes. Techniques from classical shape optimization and
calculus are shown to carry over to this framework, and are collected in generality
for future reference.
A pre-shape parameterization tracking problem class for mesh quality is in-
troduced, which is solvable by use of pre-shape derivatives. This class allows for
non-uniform user prescribed adaptations of the shape and hold-all domain meshes.
It acts as a regularizer for classical shape objectives. Existence of regularized solu-
tions is guaranteed, and corresponding optimal pre-shapes are shown to correspond
to optimal shapes of the original problem, which additionally achieve the user pre-
scribed parameterization.
We present shape gradient system modifications, which allow simultaneous nu-
merical shape optimization with mesh quality improvement. Further, consistency
of modified pre-shape gradient systems is established. The computational burden
of our approach is limited, since additional solution of possibly larger (non-)linear
systems for regularized shape gradients is not necessary. We implement and com-
pare these pre-shape gradient regularization approaches for a 2D problem, which
is prone to mesh degeneration. As our approach does not depend on the choice of
forms to represent shape gradients, we employ and compare weak linear elasticity
and weak quasilinear p-Laplacian pre-shape gradient representations.
We also introduce a Quasi-Newton-ADM inspired algorithm for mesh quality,
which guarantees sufficient adaption of meshes to user specification during the rou-
tines. It is applicable in addition to simultaneous mesh regularization techniques.
Unrelated to mesh regularization techniques, we consider shape optimization
problems constrained by elliptic variational inequalities of the first kind, so-called
obstacle-type problems. In general, standard necessary optimality conditions cannot
be formulated in a straightforward manner for such semi-smooth shape optimization
problems. Under appropriate assumptions, we prove existence and convergence of
adjoints for smooth regularizations of the VI-constraint. Moreover, we derive shape
derivatives for the regularized problem and prove convergence to a limit object.
Based on this analysis, an efficient optimization algorithm is devised and tested
numerically.
All previous pre-shape regularization techniques are applied to a variational
inequality constrained shape optimization problem, where we also create customized
targets for increased mesh adaptation of changing embedded shapes and active set
boundaries of the constraining variational inequality.
Hybrid Modelling in general, describes the combination of at least two different methods to solve one specific task. As far as this work is concerned, Hybrid Models describe an approach to combine sophisticated, well-studied mathematical methods with Deep Neural Networks to solve parameter estimation tasks. To combine these two methods, the data structure of artifi- cially generated acceleration data of an approximate vehicle model, the Quarter-Car-Model, is exploited. Acceleration of individual components within a coupled dynamical system, can be described as a second order ordinary differential equation, including velocity and dis- placement of coupled states, scaled by spring - and damping-coefficient of the system. An appropriate numerical integration scheme can then be used to simulate discrete acceleration profiles of the Quarter-Car-Model with a random variation of the parameters of the system. Given explicit knowledge about the data structure, one can then investigate under which con- ditions it is possible to estimate the parameters of the dynamical system for a set of randomly generated data samples. We test, if Neural Networks are capable to solve parameter estima- tion problems in general, or if they can be used to solve several sub-tasks, which support a state-of-the-art parameter estimation method. Hybrid Models are presented for parameter estimation under uncertainties, including for instance measurement noise or incompleteness of measurements, which combine knowledge about the data structure and several Neural Networks for robust parameter estimation within a dynamical system.
Zeitgleich mit stetig wachsenden gesellschaftlichen Herausforderungen haben im vergangenen Jahrzehnt Sozialunternehmen stark an Bedeutung gewonnen. Sozialunternehmen verfolgen das Ziel, mit unternehmerischen Mitteln gesellschaftliche Probleme zu lösen. Da der Fokus von Sozialunternehmen nicht hauptsächlich auf der eigenen Gewinnmaximierung liegt, haben sie oftmals Probleme, geeignete Unternehmensfinanzierungen zu erhalten und Wachstumspotenziale zu verwirklichen.
Zur Erlangung eines tiefergehenden Verständnisses des Phänomens der Sozialunternehmen untersucht der erste Teil dieser Dissertation anhand von zwei Studien auf der Basis eines Experiments das Entscheidungsverhalten der Investoren von Sozialunternehmen. Kapitel 2 betrachtet daher das Entscheidungsverhalten von Impact-Investoren. Der von diesen Investoren verfolgte Investmentansatz „Impact Investing“ geht über eine reine Orientierung an Renditen hinaus. Anhand eines Experiments mit 179 Impact Investoren, die insgesamt 4.296 Investitionsentscheidungen getroffen haben, identifiziert eine Conjoint-Studie deren wichtigste Entscheidungskriterien bei der Auswahl der Sozialunternehmen. Kapitel 3 analysiert mit dem Fokus auf sozialen Inkubatoren eine weitere spezifische Gruppe von Unterstützern von Sozialunternehmen. Dieses Kapitel veranschaulicht auf der Basis des Experiments die Motive und Entscheidungskriterien der Inkubatoren bei der Auswahl von Sozialunternehmen sowie die von ihnen angebotenen Formen der nichtfinanziellen Unterstützung. Die Ergebnisse zeigen unter anderem, dass die Motive von sozialen Inkubatoren bei der Unterstützung von Sozialunternehmen unter anderem gesellschaftlicher, finanzieller oder reputationsbezogener Natur sind.
Der zweite Teil erörtert auf der Basis von zwei quantitativ empirischen Studien, inwiefern die Registrierung von Markenrechten sich zur Messung sozialer Innovationen eignet und mit finanziellem und sozialem Wachstum von sozialen Startups in Verbindung steht. Kapitel 4 erörtert, inwiefern Markenregistrierungen zur Messung von sozialen Innovationen dienen können. Basierend auf einer Textanalyse der Webseiten von 925 Sozialunternehmen (> 35.000 Unterseiten) werden in einem ersten Schritt vier Dimensionen sozialer Innovationen (Innovations-, Impact-, Finanz- und Skalierbarkeitsdimension) ermittelt. Darauf aufbauend betrachtet dieses Kapitel, wie verschiedene Markencharakteristiken mit den Dimensionen sozialer Innovationen zusammenhängen. Die Ergebnisse zeigen, dass insbesondere die Anzahl an registrierten Marken als Indikator für soziale Innovationen (alle Dimensionen) dient. Weiterhin spielt die geografische Reichweite der registrierten Marken eine wichtige Rolle. Aufbauend auf den Ergebnissen von Kapitel 4 untersucht Kapitel 5 den Einfluss von Markenregistrierungen in frühen Unternehmensphasen auf die weitere Entwicklung der hybriden Ergebnisse von sozialen Startups. Im Detail argumentiert Kapitel 5, dass sowohl die Registrierung von Marken an sich als auch deren verschiedene Charakteristiken unterschiedlich mit den sozialen und ökonomischen Ergebnissen von sozialen Startups in Verbindung stehen. Anhand eines Datensatzes von 485 Sozialunternehmen zeigen die Analysen aus Kapitel 5, dass soziale Startups mit einer registrierten Marke ein vergleichsweise höheres Mitarbeiterwachstum aufweisen und einen größeren gesellschaftlichen Beitrag leisten.
Die Ergebnisse dieser Dissertation weiten die Forschung im Social Entrepreneurship-Bereich weiter aus und bieten zahlreiche Implikationen für die Praxis. Während Kapitel 2 und 3 das Verständnis über die Eigenschaften von nichtfinanziellen und finanziellen Unterstützungsorganisationen von Sozialunternehmen vergrößern, schaffen Kapitel 4 und 5 ein größeres Verständnis über die Bedeutung von Markenanmeldungen für Sozialunternehmen.
Die Effekte diverser Hormone auf das Sozialverhalten von Männern und Frauen sind nicht vollständig geklärt, da eine genaue Messung dieser, sowie eine Ableitung kausaler Zusammenhänge, die Forschung seither vor Herausforderungen stellt. Umso wichtiger sind Studien, welche versuchen für konfundierende Aspekte zu kontrollieren und die hormonellen oder endokrinen Effekte auf das Sozialverhalten und die soziale Kognition zu untersuchen. Während Studien bereits Effekte von akutem Stress auf Sozialverhalten zeigten, sind die zugrundeliegenden neurobiologischen Mechanismen nicht vollständig bekannt, da hierfür ein rein pharmakologischer Ansatz von Nöten wäre. Die wenigen Studien, die einen solchen wählten, zeigen konträre Befunde. Bisherige Untersuchungen mit psychosozialen Stressoren lassen jedoch prosoziale Tendenzen nach Stress sowohl für Männer als auch für Frauen vermuten. Darüber hinaus sind auch Untersuchungen zu weiblichen Geschlechtshormonen und ihrem Einfluss auf Sozialverhalten sowie die soziale Kognition bei Frauen besonders herausfordernd durch die hormonellen Schwankungen während des Menstruationszyklus oder auch Veränderungen durch die Einnahme oraler Kontrazeptiva. Studien die sowohl Zyklusphasen als auch die Effekte von oralen Kontrazeptiva untersuchten, deuten aber bereits auf Unterschiede zwischen den verschiedenen Phasen, sowie Frauen mit natürlichem Zyklus und Einnahme oraler Kontrazeptiva hin.
Der theoretische Teil beschreibt die Grundlagen zur Stressreaktion des Menschen und die hormonellen Veränderungen weiblicher Geschlechtshormone. Folgend, soll ein Kapitel zur aktuellen Forschungslage zu Effekten von akutem Stress auf Sozialverhalten und die soziale Kognition einen Überblick über die bisherige Befundlage schaffen. Die erste empirische Studie, welche die Effekte von Hydrocortison auf das Sozialverhalten und die Emotionserkennung untersucht, soll anschließend in diese aktuelle Befundlage eingeordnet werden und zu der weniger erforschten Sparte der pharmakologischen Studien beitragen. Die zweite empirische Studie befasst sich folgend mit den Effekten weiblicher Geschlechtshormone auf Sozialverhalten und Empathie, genauer wie auch Zyklusphasen und orale Kontrazeptiva (über Hormone vermittelt) einen Einfluss bei Frauen nehmen. Abschließend sollen die Effekte von Stresshormonen bei Männern, und modulierende Eigenschaften weiblicher Geschlechtshormone, Zyklusphasen und oraler Kontrazeptiva bei Frauen, jeweils in Hinblick auf Sozialverhalten und die soziale Kognition diskutiert werden.
Forest inventories provide significant monitoring information on forest health, biodiversity,
resilience against disturbance, as well as its biomass and timber harvesting potential. For this
purpose, modern inventories increasingly exploit the advantages of airborne laser scanning (ALS)
and terrestrial laser scanning (TLS).
Although tree crown detection and delineation using ALS can be seen as a mature discipline, the
identification of individual stems is a rarely addressed task. In particular, the informative value of
the stem attributes—especially the inclination characteristics—is hardly known. In addition, a lack
of tools for the processing and fusion of forest-related data sources can be identified. The given
thesis addresses these research gaps in four peer-reviewed papers, while a focus is set on the
suitability of ALS data for the detection and analysis of tree stems.
In addition to providing a novel post-processing strategy for geo-referencing forest inventory plots,
the thesis could show that ALS-based stem detections are very reliable and their positions are
accurate. In particular, the stems have shown to be suited to study prevailing trunk inclination
angles and orientations, while a species-specific down-slope inclination of the tree stems and a
leeward orientation of conifers could be observed.
Agricultural monitoring is necessary. Since the beginning of the Holocene, human agricultural
practices have been shaping the face of the earth, and today around one third of the ice-free land
mass consists of cropland and pastures. While agriculture is necessary for our survival, the
intensity has caused many negative externalities, such as enormous freshwater consumption, the
loss of forests and biodiversity, greenhouse gas emissions as well as soil erosion and degradation.
Some of these externalities can potentially be ameliorated by careful allocation of crops and
cropping practices, while at the same time the state of these crops has to be monitored in order
to assess food security. Modern day satellite-based earth observation can be an adequate tool to
quantify abundance of crop types, i.e., produce spatially explicit crop type maps. The resources to
do so, in terms of input data, reference data and classification algorithms have been constantly
improving over the past 60 years, and we live now in a time where fully operational satellites
produce freely available imagery with often less than monthly revisit times at high spatial
resolution. At the same time, classification models have been constantly evolving from
distribution based statistical algorithms, over machine learning to the now ubiquitous deep
learning.
In this environment, we used an explorative approach to advance the state of the art of crop
classification. We conducted regional case studies, focused on the study region of the Eifelkreis
Bitburg-Prüm, aiming to develop validated crop classification toolchains. Because of their unique
role in the regional agricultural system and because of their specific phenologic characteristics
we focused solely on maize fields.
In the first case study, we generated reference data for the years 2009 and 2016 in the study
region by drawing polygons based on high resolution aerial imagery, and used these in
conjunction with RapidEye imagery to produce high resolution maize maps with a random forest
classifier and a gaussian blur filter. We were able to highlight the importance of careful residual
analysis, especially in terms of autocorrelation. As an end result, we were able to prove that, in
spite of the severe limitations introduced by the restricted acquisition windows due to cloud
coverage, high quality maps could be produced for two years, and the regional development of
maize cultivation could be quantified.
In the second case study, we used these spatially explicit datasets to link the expansion of biogas
producing units with the extended maize cultivation in the area. In a next step, we overlayed the
maize maps with soil and slope rasters in order to assess spatially explicit risks of soil compaction
and erosion. Thus, we were able to highlight the potential role of remote sensing-based crop type
classification in environmental protection, by producing maps of potential soil hazards, which can
be used by local stakeholders to reallocate certain crop types to locations with less associated
risk.
In our third case study, we used Sentinel-1 data as input imagery, and official statistical records
as maize reference data, and were able to produce consistent modeling input data for four
consecutive years. Using these datasets, we could train and validate different models in spatially
iv
and temporally independent random subsets, with the goal of assessing model transferability. We
were able to show that state-of-the-art deep learning models such as UNET performed
significantly superior to conventional models like random forests, if the model was validated in a
different year or a different regional subset. We highlighted and discussed the implications on
modeling robustness, and the potential usefulness of deep learning models in building fully
operational global crop classification models.
We were able to conclude that the first major barrier for global classification models is the
reference data. Since most research in this area is still conducted with local field surveys, and only
few countries have access to official agricultural records, more global cooperation is necessary to
build harmonized and regionally stratified datasets. The second major barrier is the classification
algorithm. While a lot of progress has been made in this area, the current trend of many appearing
new types of deep learning models shows great promise, but has not yet consolidated. There is
still a lot of research necessary, to determine which models perform the best and most robust,
and are at the same time transparent and usable by non-experts such that they can be applied
and used effortlessly by local and global stakeholders.
This thesis is concerned with two classes of optimization problems which stem
mainly from statistics: clustering problems and cardinality-constrained optimization problems. We are particularly interested in the development of computational techniques to exactly or heuristically solve instances of these two classes
of optimization problems.
The minimum sum-of-squares clustering (MSSC) problem is widely used
to find clusters within a set of data points. The problem is also known as
the $k$-means problem, since the most prominent heuristic to compute a feasible
point of this optimization problem is the $k$-means method. In many modern
applications, however, the clustering suffers from uncertain input data due to,
e.g., unstructured measurement errors. The reason for this is that the clustering
result then represents a clustering of the erroneous measurements instead of
retrieving the true underlying clustering structure. We address this issue by
applying robust optimization techniques: we derive the strictly and $\Gamma$-robust
counterparts of the MSSC problem, which are as challenging to solve as the
original model. Moreover, we develop alternating direction methods to quickly
compute feasible points of good quality. Our experiments reveal that the more
conservative strictly robust model consistently provides better clustering solutions
than the nominal and the less conservative $\Gamma$-robust models.
In the context of clustering problems, however, using only a heuristic solution
comes with severe disadvantages regarding the interpretation of the clustering.
This motivates us to study globally optimal algorithms for the MSSC problem.
We note that although some algorithms have already been proposed for this
problem, it is still far from being “practically solved”. Therefore, we propose
mixed-integer programming techniques, which are mainly based on geometric
ideas and which can be incorporated in a
branch-and-cut based algorithm tailored
to the MSSC problem. Our numerical experiments show that these techniques
significantly improve the solution process of a
state-of-the-art MINLP solver
when applied to the problem.
We then turn to the study of cardinality-constrained optimization problems.
We consider two famous problem instances of this class: sparse portfolio optimization and sparse regression problems. In many modern applications, it is common
to consider problems with thousands of variables. Therefore, globally optimal
algorithms are not always computationally viable and the study of sophisticated
heuristics is very desirable. Since these problems have a discrete-continuous
structure, decomposition methods are particularly well suited. We then apply a
penalty alternating direction method that explores this structure and provides
very good feasible points in a reasonable amount of time. Our computational
study shows that our methods are competitive to
state-of-the-art solvers and heuristics.
Even though in most cases time is a good metric to measure costs of algorithms, there are cases where theoretical worst-case time and experimental running time do not match. Since modern CPUs feature an innate memory hierarchy, the location of data is another factor to consider. When most operations of an algorithm are executed on data which is already in the CPU cache, the running time is significantly faster than algorithms where most operations have to load the data from the memory. The topic of this thesis is a new metric to measure costs of algorithms called memory distance—which can be seen as an abstraction of the just mentioned aspect. We will show that there are simple algorithms which show a discrepancy between measured running time and theoretical time but not between measured time and memory distance. Moreover we will show that in some cases it is sufficient to optimize the input of an algorithm with regard to memory distance (while treating the algorithm as a black box) to improve running times. Further we show the relation between worst-case time, memory distance and space and sketch how to define "the usual" memory distance complexity classes.
The Second Language Acquisition of English Non-Finite Complement Clauses – A Usage-Based Perspective
(2022)
One of the most essential hypotheses of usage-based theories and many constructionist approaches to language is that language entails the piecemeal learning of constructions on the basis of general cognitive mechanisms and exposure to the target language in use (Ellis 2002; Tomasello 2003). However, there is still a considerable lack of empirical research on the emergence and mental representation of constructions in second language (L2) acquisition. One crucial question that arises, for instance, is whether L2 learners’ knowledge of a construction corresponds to a native-like mapping of form and meaning and, if so, to what extent this representation is shaped by usage. For instance, it is unclear how learners ‘build’ constructional knowledge, i.e. which pieces of frequency-, form- and meaning-related information become relevant for the entrenchment and schematisation of a L2 construction.
To address these issues, the English catenative verb construction was used as a testbed phenomenon. This idiosyncratic complex construction is comprised of a catenative verb and a non-finite complement clause (see Huddleston & Pullum 2002), which is prototypically a gerund-participial (henceforth referred to as ‘target-ing’ construction) or a to-infinitival complement (‘target-to’ construction):
(1) She refused to do her homework.
(2) Laura kept reading love stories.
(3) *He avoids to listen to loud music.
This construction is particularly interesting because learners often show choices of a complement type different from those of native speakers (e.g. Gries & Wulff 2009; Martinez‐Garcia & Wulff 2012) as illustrated in (3) and is commonly claimed to be difficult to be taught by explicit rules (see e.g. Petrovitz 2001).
By triangulating different types of usage data (corpus and elicited production data) and analysing these by multivariate statistical tests, the effects of different usage-related factors (e.g. frequency, proficiency level of the learner, semantic class of verb, etc.) on the representation and development of the catenative verb construction and its subschemas (i.e. target-to and target-ing construction) were examined. In particular, it was assessed whether they can predict a native-like form-meaning pairing of a catenative verb and non-finite complement.
First, all studies were able to show a robust effect of frequency on the complement choice. Frequency does not only lead to the entrenchment of high-frequency exemplars of the construction but is also found to motivate a taxonomic generalisation across related exemplars and the representation of a more abstract schema. Second, the results indicate that the target-to construction, due to its higher type and token frequency, has a high degree of schematicity and productivity than the target-ing construction for the learners, which allows for analogical comparisons and pattern extension with less entrenched exemplars. This schema is likely to be overgeneralised to (less frequent) target-ing verbs because the learners perceive formal and semantic compatibility between the unknown/infrequent verb and this pattern.
Furthermore, the findings present evidence that less advanced learners (A2-B2) make more coarse-grained generalisations, which are centred around high-frequency and prototypical exemplars/low-scope patterns. In the case of high-proficiency learners (C1-C2), not only does the number of native-like complement choices increase but relational information, such as the semantic subclasses of the verb, form-function contingency and other factors, becomes also relevant for a target-like choice. Thus, the results suggests that with increasing usage experience learners gradually develop a more fine-grained, interconnected representation of the catenative verb construction, which gains more resemblance to the form-meaning mappings of native speakers.
Taken together, these insights highlight the importance for language learning and teaching environments to acknowledge that L2 knowledge is represented in the form of highly interconnected form-meaning pairings, i.e. constructions, that can be found on different levels of abstraction and complexity.