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The trophic niche is a life trait that identifies the consumer’s position in a local food web. Several factors, such as ontogeny, competitive ability and resource availability contribute in shaping species trophic niches. To date, information on the diet of European Hydromantes salamanders are only available for a limited number of species, no dietary studies have involved more than one species of the genus at a time, and there are limited evidences on how multiple factors interact in determining diet variation. In this study we examined the diet of multiple populations of six out of the eight European cave salamanders, providing the first data on the diet for five of them. In addition, we assessed whether these closely related generalist species show similar diet and, for each species, we tested whether season, age class or sex influence the number and the type of prey consumed. Stomach condition (empty/full) and the number of prey consumed were strongly related to seasonality and to the activity level of individuals. Empty stomachs were more frequent in autumn, in individuals far from cave entrance and in juveniles. Diet composition was significantly different among species. Hydromantes imperialis and H. supramontis were the most generalist species; H. flavus and H. sarrabusensis fed mostly on Hymenoptera and Coleoptera Staphylinidae, while H. genei and H. ambrosii mostly consumed Arachnida and Endopterygota larvae. Furthermore, we detected seasonal shifts of diet in the majority of the species examined. Conversely, within each species, we did not find diet differences between females, males and juveniles. Although being assumed to have very similar dietary habits, here Hydromantes species were shown to be characterized by a high divergence in diet composition and in the stomach condition of individuals.

In the context of accelerated global socio-environmental change, the Water-Energy-Food Nexus has received increasing attention within science and international politics by promoting integrated resource governance. This study explores the scientific nexus debates from a discourse analytical perspective to reveal knowledge and power relations as well as geographical settings of nexus research. We also investigate approaches to socio-nature relations that influence nexus research and subsequent political implications. Our findings suggest that the leading nexus discourse is dominated by natural scientific perspectives and a neo-Malthusian framing of environmental challenges. Accordingly, the promoted cross-sectoral nexus approach to resource governance emphasizes efficiency, security, future sustainability, and poverty reduction. Water, energy, and food are conceived as global trade goods that require close monitoring, management and control, to be achieved via quantitative assessments and technological interventions. Within the less visible discourse, social scientific perspectives engage with the social, political, and normative elements of the Water-Energy-Food Nexus. These perspectives criticize the dominant nexus representation for itsmanagerial, neoliberal, and utilitarian approach to resource governance. The managerial framing is critiqued for masking power relations and social inequalities, while alternative framings acknowledge the political nature of resource governance and socio-nature relations. The spatial dimensions of the nexus debate are also discussed. Notably, the nexus is largely shaped by western knowledge, yet applied mainly in specific regions of the Global South. In order for the nexus to achieve integrative solutions for sustainability, the debate needs to overcome its current discursive and spatial separations. To this end, we need to engage more closely with alternative nexus discourses, embrace epistemic pluralism and encourage multi-perspective debates about the socio-nature relations we actually intend to promote.

External capital plays an important role in financing entrepreneurial ventures, due to limited internal capital sources. An important external capital provider for entrepreneurial ventures are venture capitalists (VCs). VCs worldwide are often confronted with thousands of proposals of entrepreneurial ventures per year and must choose among all of these companies in which to invest. Not only do VCs finance companies at their early stages, but they also finance entrepreneurial companies in their later stages, when companies have secured their first market success. That is why this dissertation focuses on the decision-making behavior of VCs when investing in later-stage ventures. This dissertation uses both qualitative as well as quantitative research methods in order to provide answer to how the decision-making behavior of VCs that invest in later-stage ventures can be described.
Based on qualitative interviews with 19 investment professionals, the first insight gained is that for different stages of venture development, different decision criteria are applied. This is attributed to different risks and goals of ventures at different stages, as well as the different types of information available. These decision criteria in the context of later-stage ventures contrast with results from studies that focus on early-stage ventures. Later-stage ventures possess meaningful information on financials (revenue growth and profitability), the established business model, and existing external investors that is not available for early-stage ventures and therefore constitute new decision criteria for this specific context.
Following this identification of the most relevant decision criteria for investors in the context of later-stage ventures, a conjoint study with 749 participants was carried out to understand the relative importance of decision criteria. The results showed that investors attribute the highest importance to 1) revenue growth, (2) value-added of products/services for customers, and (3) management team track record, demonstrating differences when compared to decision-making studies in the context of early-stage ventures.
Not only do the characteristics of a venture influence the decision to invest, additional indirect factors, such as individual characteristics or characteristics of the investment firm, can influence individual decisions. Relying on cognitive theory, this study investigated the influence of various individual characteristics on screening decisions and found that both investment experience and entrepreneurial experience have an influence on individual decision-making behavior. This study also examined whether goals, incentive structures, resources, and governance of the investment firm influence decision making in the context of later-stage ventures. This study particularly investigated two distinct types of investment firms, family offices and corporate venture capital funds (CVC), which have unique structures, goals, and incentive systems. Additional quantitative analysis showed that family offices put less focus on high-growth firms and whether reputable investors are present. They tend to focus more on the profitability of a later-stage venture in the initial screening. The analysis showed that CVCs place greater importance on product and business model characteristics than other investors. CVCs also favor later-stage ventures with lower revenue growth rates, indicating a preference for less risky investments. The results provide various insights for theory and practice.

There are large health, societal, and economic costs associated with attrition from psychological services. The recently emerged, innovative statistical tool of complex network analysis was used in the present proof-of-concept study to improve the prediction of attrition. Fifty-eight patients undergoing psychological treatment for mood or anxiety disorders were assessed using Ecological Momentary Assessments four times a day for two weeks before treatment (3,248 measurements). Multilevel vector autoregressive models were employed to compute dynamic symptom networks. Intake variables and network parameters (centrality measures) were used as predictors for dropout using machine-learning algorithms. Networks for patients differed significantly between completers and dropouts. Among intake variables, initial impairment and sex predicted dropout explaining 6% of the variance. The network analysis identified four additional predictors: Expected force of being excited, outstrength of experiencing social support, betweenness of feeling nervous, and instrength of being active. The final model with the two intake and four network variables explained 32% of variance in dropout and identified 47 out of 58 patients correctly. The findings indicate that patients" dynamic network structures may improve the prediction of dropout. When implemented in routine care, such prediction models could identify patients at risk for attrition and inform personalized treatment recommendations.

Reptiles belong to a taxonomic group characterized by increasing worldwide population declines. However, it has not been until comparatively recent years that public interest in these taxa has increased, and conservation measures are starting to show results. While many factors contribute to these declines, environmental pollution, especially in form of pesticides, has seen a strong increase in the last few decades, and is nowadays considered a main driver for reptile diversity loss. In light of the above, and given that reptiles are extremely underrepresented in ecotoxicological studies regarding the effects of plant protection products, this thesis aims at studying the impacts of pesticide exposure in reptiles, by using the Common wall lizard (Podarcis muralis) as model species. In a first approach, I evaluated the risk of pesticide exposure for reptile species within the European Union, as a means to detect species with above average exposure probabilities and to detect especially sensitive reptile orders. While helpful to detect species at risk, a risk evaluation is only the first step towards addressing this problem. It is thus indispensable to identify effects of pesticide exposure in wildlife. For this, the use of enzymatic biomarkers has become a popular method to study sub-individual responses, and gain information regarding the mode of action of chemicals. However, current methodologies are very invasive. Thus, in a second step, I explored the use of buccal swabs as a minimally invasive method to detect changes in enzymatic biomarker activity in reptiles, as an indicator for pesticide uptake and effects at the sub-individual level. Finally, the last part of this thesis focuses on field data regarding pesticide exposure and its effects on reptile wildlife. Here, a method to determine pesticide residues in food items of the Common wall lizard was established, as a means to generate data for future dietary risk assessments. Subsequently, a field study was conducted with the aim to describe actual effects of pesticide exposure on reptile populations at different levels.

The economic growth theory analyses which factors affect economic growth
and tries to analyze how it can last. A popular neoclassical growth model
is the Ramsey-Cass-Koopmans model, which aims to determine how much
of its income a nation or an economy should save in order to maximize its
welfare.
In this thesis, we present and analyze an extended capital accumulation equation of a spatial version of the Ramsey model, balancing diffusive and agglomerative effects. We model the capital mobility in space via a nonlocal
diffusion operator which allows for jumps of the capital stock from one lo-
cation to an other. Moreover, this operator smooths out heterogeneities in
the factor distributions slower, which generated a more realistic behavior of
capital flows. In addition to that, we introduce an endogenous productivity-
production operator which depends on time and on the capital distribution
in space. This operator models the technological progress of the economy.
The resulting mathematical model is an optimal control problem under a
semilinear parabolic integro-differential equation with initial and volume constraints, which are a nonlocal analog to local boundary conditions, and box-constraints on the state and the control variables. In this thesis, we consider
this problem on a bounded and unbounded spatial domain, in both cases with
a finite time horizon. We derive existence results of weak solutions for the
capital accumulation equations in both settings and we proof the existence
of a Ramsey equilibrium in the unbounded case. Moreover, we solve the
optimal control problem numerically and discuss the results in the economic
context.

Surveys are commonly tailored to produce estimates of aggregate statistics with a desired level of precision. This may lead to very small sample sizes for subpopulations of interest, defined geographically or by content, which are not incorporated into the survey design. We refer to subpopulations where the sample size is too small to provide direct estimates with adequate precision as small areas or small domains. Despite the small sample sizes, reliable small area estimates are needed for economic and political decision making. Hence, model-based estimation techniques are used which increase the effective sample size by borrowing strength from other areas to provide accurate information for small areas. The paragraph above introduced small area estimation as a field of survey statistics where two conflicting philosophies of statistical inference meet: the design-based and the model-based approach. While the first approach is well suited for the precise estimation of aggregate statistics, the latter approach furnishes reliable small area estimates. In most applications, estimates for both large and small domains based on the same sample are needed. This poses a challenge to the survey planner, as the sampling design has to reflect different and potentially conflicting requirements simultaneously. In order to enable efficient design-based estimates for large domains, the sampling design should incorporate information related to the variables of interest. This may be achieved using stratification or sampling with unequal probabilities. Many model-based small area techniques require an ignorable sampling design such that after conditioning on the covariates the variable of interest does not contain further information about the sample membership. If this condition is not fulfilled, biased model-based estimates may result, as the model which holds for the sample is different from the one valid for the population. Hence, an optimisation of the sampling design without investigating the implications for model-based approaches will not be sufficient. Analogously, disregarding the design altogether and focussing only on the model is prone to failure as well. Instead, a profound knowledge of the interplay between the sample design and statistical modelling is a prerequisite for implementing an effective small area estimation strategy. In this work, we concentrate on two approaches to address this conflict. Our first approach takes the sampling design as given and can be used after the sample has been collected. It amounts to incorporate the survey design into the small area model to avoid biases stemming from informative sampling. Thus, once a model is validated for the sample, we know that it holds for the population as well. We derive such a procedure under a lognormal mixed model, which is a popular choice when the support of the dependent variable is limited to positive values. Besides, we propose a three pillar strategy to select the additional variable accounting for the design, based on a graphical examination of the relationship, a comparison of the predictive accuracy of the choices and a check regarding the normality assumptions.rnrnOur second approach to deal with the conflict is based on the notion that the design should allow applying a wide variety of analyses using the sample data. Thus, if the use of model-based estimation strategies can be anticipated before the sample is drawn, this should be reflected in the design. The same applies for the estimation of national statistics using design-based approaches. Therefore, we propose to construct the design such that the sampling mechanism is non-informative but allows for precise design-based estimates at an aggregate level.

The Harmonic Faber Operator
(2018)

P. K. Suetin points out in the beginning of his monograph "Faber
Polynomials and Faber Series" that Faber polynomials play an important
role in modern approximation theory of a complex variable as they
are used in representing analytic functions in simply connected domains,
and many theorems on approximation of analytic functions are proved
with their help [50].
In 1903, the Faber polynomials were firstly discovered by G. Faber. It was Faber's aim to find a generalisation of Taylor
series of holomorphic functions in the open unit disc D
in the following way. As any holomorphic function in D
has a Taylor series representation
f(z)=\sum_{\nu=0}^{\infty}a_{\nu}z^{\nu} (z\in\D)
converging locally uniformly inside D, for a simply connected
domain G, Faber wanted to determine a system of polynomials (Q_n)
such that each function f being holomorphic in G can be expanded
into a series
f=\sum_{\nu=0}^{\infty}b_{\nu}Q_{\nu}
converging locally uniformly inside G. Having this goal in mind,
Faber considered simply connected domains bounded by an analytic Jordan
curve. He constructed a system of polynomials (F_n)
with this property. These polynomials F_n were named after him
as Faber polynomials. In the preface of [50],
a detailed summary of results concerning Faber polynomials and results
obtained by the aid of them is given.
An important application of Faber polynomials is e.g. the transfer
of known assertions concerning polynomial approximation of functions
belonging to the disc algebra to results of the approximation of functions
being continuous on a compact continuum K which contains at least
two points and has a connected complement and being holomorphic in
the interior of K. In this field, the Faber operator
denoted by T turns out to be a powerful tool (for
an introduction, see e.g. D. Gaier's monograph). It
assigns a polynomial of degree at most n given in the monomial
basis \sum_{\nu=0}^{n}a_{\nu}z^{\nu} with a polynomial of degree
at most n given in the basis of Faber polynomials \sum_{\nu=0}^{n}a_{\nu}F_{\nu}.
If the Faber operator is continuous with respect to the uniform norms,
it has a unique continuous extension to an operator mapping the disc
algebra onto the space of functions being continuous on the whole
compact continuum and holomorphic in its interior. For all f being
element of the disc algebra and all polynomials P, via the obvious
estimate for the uniform norms
||T(f)-T(P)||<= ||T|| ||f-P||,
it can be seen that the original task of approximating F=T(f)
by polynomials is reduced to the polynomial approximation of the function
f. Therefore, the question arises under which conditions the Faber
operator is continuous and surjective. A fundamental result in this
regard was established by J. M. Anderson and J. Clunie who showed
that if the compact continuum is bounded by a rectifiable Jordan curve
with bounded boundary rotation and free from cusps, then the Faber
operator with respect to the uniform norms is a topological isomorphism.
Now, let f be a harmonic function in D.
Similar as above, we find that f has a uniquely determined representation
f=\sum_{\nu=-\infty}^{\infty}a_{\nu}p_{\nu}
converging locally uniformly inside D where p_{n}(z)=z^{n}
for n\in\N_{0} and p_{-n}(z)=\overline{z}^{n}
for n\in\N}. One may ask whether there is an analogue for
harmonic functions on simply connected domains G. Indeed, for a
domain G bounded by an analytic Jordan curve, the conjecture that
each function f being harmonic in G has a uniquely determined
representation
f=\sum_{\nu=-\infty}^{\infty}b_{\nu}F_{\nu}
where F_{-n}(z)=\overline{F_{n}(z\)} for n\inN,
converging locally uniformly inside G, holds true.
Let now K be a compact continuum containing at least two points
and having a connected complement. A main component of this thesis
will be the examination of the harmonic Faber operator mapping a harmonic
polynomial given in the basis of the harmonic monomials \sum_{\nu=-n}^{n}a_{\nu}p_{\nu}
to a harmonic polynomial given as \sum_{\nu=-n}^{n}a_{\nu}F_{\nu}.
If this operator, which is based on an idea of J. Müller,
is continuous with respect to the uniform norms, it has a unique continuous
extension to an operator mapping the functions being continuous on
\partial\D onto the continuous functions on K being
harmonic in the interior of K. Harmonic Faber polynomials and the
harmonic Faber operator will be the objects accompanying us throughout
our whole discussion.
After having given an overview about notations and certain tools we
will use in our consideration in the first chapter, we begin our studies
with an introduction to the Faber operator and the harmonic Faber
operator. We start modestly and consider domains bounded by an analytic
Jordan curve. In Section 2, as a first
result, we will show that, for such a domain G, the harmonic Faber
operator has a unique continuous extension to an operator mapping
the space of the harmonic functions in D onto the space
of the harmonic functions in G, and moreover, the harmonic Faber
operator is an isomorphism with respect to the topologies of locally
uniform convergence. In the further sections of this chapter, we illumine
the behaviour of the (harmonic) Faber operator on certain function
spaces.
In the third chapter, we leave the situation of compact continua bounded
by an analytic Jordan curve. Instead we consider closures of domains
bounded by Jordan curves having a Dini continuous curvature. With
the aid of the concept of compact operators and the Fredholm alternative,
we are able to show that the harmonic Faber operator is a topological
isomorphism.
Since, in particular, the main result of the third chapter holds true
for closures K of domains bounded by analytic Jordan curves, we
can make use of it to obtain new results concerning the approximation
of functions being continuous on K and harmonic in the interior
of K by harmonic polynomials. To do so, we develop techniques applied
by L. Frerick and J. Müller in [11] and adjust them to
our setting. So, we can transfer results about the classic Faber operator
to the harmonic Faber operator.
In the last chapter, we will use the theory of harmonic Faber polynomials
to solve certain Dirichlet problems in the complex plane. We pursue
two different approaches: First, with a similar philosophy as in [50],
we develop a procedure to compute the coefficients of a series \sum_{\nu=-\infty}^{\infty}c_{\nu}F_{\nu}
converging uniformly to the solution of a given Dirichlet problem.
Later, we will point out how semi-infinite programming with harmonic
Faber polynomials as ansatz functions can be used to get an approximate
solution of a given Dirichlet problem. We cover both approaches first
from a theoretical point of view before we have a focus on the numerical
implementation of concrete examples. As application of the numerical
computations, we considerably obtain visualisations of the concerned
Dirichlet problems rounding out our discussion about the harmonic
Faber polynomials and the harmonic Faber operator.

The forward effect of testing refers to the finding that retrieval practice of previously studied information increases retention of subsequently studied other information. It has recently been hypothesized that the forward effect (partly) reflects the result of a reset-of-encoding (ROE) process. The proposal is that encoding efficacy decreases with an increase in study material, but testing of previously studied information resets the encoding process and makes the encoding of the subsequently studied information as effective as the encoding of the previously studied information. The goal of the present study was to verify the ROE hypothesis on an item level basis. An experiment is reported that examined the effects of testing in comparison to restudy on items’ serial position curves. Participants studied three lists of items in each condition. In the testing condition, participants were tested immediately on non-target lists 1 and 2, whereas in the restudy condition, they restudied lists 1 and 2. In both conditions, participants were tested immediately on target list 3. Influences of condition and items’ serial learning position on list 3 recall were analyzed. The results showed the forward effect of testing and furthermore that this effect varies with items’ serial list position. Early target list items at list primacy positions showed a larger enhancement effect than middle and late target list items at non-primacy positions. The results are consistent with the ROE hypothesis on an item level basis. The generalizability of the ROE hypothesis across different experimental tasks, like the list-method directed-forgetting task, is discussed.

Academic achievement is a central outcome in educational research, both in and outside higher education, has direct effects on individual’s professional and financial prospects and a high individual and public return on investment. Theories comprise cognitive as well as non-cognitive influences on achievement. Two examples frequently investigated in empirical research are knowledge (as a cognitive determinant) and stress (as a non-cognitive determinant) of achievement. However, knowledge and stress are not stable, what raises questions as to how temporal dynamics in knowledge on the one hand and stress on the other contribute to achievement. To study these contributions in the present doctoral dissertation, I used meta-analysis, latent profile transition analysis, and latent state-trait analysis. The results support the idea of knowledge acquisition as a cumulative and long-term process that forms the basis for academic achievement and conceptual change as an important mechanism for the acquisition of knowledge in higher education. Moreover, the findings suggest that students’ stress experiences in higher education are subject to stable, trait-like influences, as well as situational and/or interactional, state-like influences which are differentially related to achievement and health. The results imply that investigating the causal networks between knowledge, stress, and academic achievement is a promising strategy for better understanding academic achievement in higher education. For this purpose, future studies should use longitudinal designs, randomized controlled trials, and meta-analytical techniques. Potential practical applications include taking account of students’ prior knowledge in higher education teaching and decreasing stress among higher education students.