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The main aim of "Her Idoll Selfe"? Shaping Identity in Early Modern Women- Self-Writings is to offer fresh readings of as yet little-read early modern women- texts. I look at a variety of texts that are either explicitly concerned with the constitution of the writer- self, such as the autobiographies by Lady Grace Mildmay and Martha Moulsworth, or in which the preoccupation with the self is of a more indirect nature, as in the mothers" advice books by Elizabeth Grymeston, Dorothy Leigh, Elizabeth Richardson or the anonymous M. R., or even in women- poetry, drama and religious verse. I situate the texts in the context of early modern discourses of femininity and subjectivity to pursue the question in how far it was possible for early modern women to achieve a sense of agency in spite of their culturally marginal position. In that, my readings aim to contribute to the ongoing critical process of decentring the early modern period. At the same time, I draw on contemporary theory as a methodological tool that can open up further dimensions of the texts, especially in places where the texts provide clues and parallels that lend themselves to a theoretical approach. Conversely, the texts themselves shed interesting light on feminist and poststructuralist theory and can serve as testing grounds for the current critical fascination with fragmentation and hybridity. Having outlined the theoretical and methodological framework of my study, I then analyse the women- writings with reference to a matrix of paradigmatic dimensions that encompass their most prominently recurring themes: the notion of writing the self, relationships between self and other, demarcations of private and public, the women- notorious preoccupation with self-loss and death, as well as the recurrent theme of the "golden meane". I suggest that this motif can provide the vital cue to early modern women- constitution of self. The idea of a precarious "golden meane" links in with to parallel discourses of moderation and balance at the time, but reinterprets them in a manner that can present a workable and innovative paradigm of subjectivity. Instead of subscribing to a model of decentred selfhood, early modern women- presentations of self suggest that a concluding but contested compromise is a workable strategy to achieve a form of selfhood that can responsibly be lived with.
Statistical matching offers a way to broaden the scope of analysis without increasing respondent burden and costs. These would result from conducting a new survey or adding variables to an existing one. Statistical matching aims at combining two datasets A and B referring to the same target population in order to analyse variables, say Y and Z, together, that initially were not jointly observed. The matching is performed based on matching variables X that correspond to common variables present in both datasets A and B. Furthermore, Y is only observed in B and Z is only observed in A. To overcome the fact that no joint information on X, Y and Z is available, statistical matching procedures have to rely on suitable assumptions. Therefore, to yield a theoretical foundation for statistical matching, most procedures rely on the conditional independence assumption (CIA), i.e. given X, Y is independent of Z.
The goal of this thesis is to encompass both the statistical matching process and the analysis of the matched dataset. More specifically, the aim is to estimate a linear regression model for Z given Y and possibly other covariates in data A. Since the validity of the assumptions underlying the matching process determine the validity of the obtained matched file, the accuracy of statistical inference is determined by the suitability of the assumptions. By putting the focus on these assumptions, this work proposes a systematic categorisation of approaches to statistical matching by relying on graphical representations in form of directed acyclic graphs. These graphs are particularly useful in representing dependencies and independencies which are at the heart of the statistical matching problem. The proposed categorisation distinguishes between (a) joint modelling of the matching and the analysis (integrated approach), and (b) matching subsequently followed by statistical analysis of the matched dataset (classical approach). Whereas the classical approach relies on the CIA, implementations of the integrated approach are only valid if they converge, i.e. if the specified models are identifiable and, in the case of MCMC implementations, if the algorithm converges to a proper distribution.
In this thesis an implementation of the integrated approach is proposed, where the imputation step and the estimation step are jointly modelled through a fully Bayesian MCMC estimation. It is based on a linear regression model for Z given Y and accounts for both a linear regression model and a random effects model for Y. Furthermore, it yields its validity when the instrumental variable assumption (IVA) holds. The IVA corresponds to: (a) Z is independent of a subset X’ of X given Y and X*, where X* = X\X’ and (b) Y is correlated with X’ given X*. The proof, that the joint Bayesian modelling of both the model for Z and the model for Y through an MCMC simulation converges to a proper distribution is provided in this thesis. In a first model-based simulation study, the proposed integrated Bayesian procedure is assessed with regard to the data situation, convergence issues, and underlying assumptions. Special interest lies in the investigation of the interplay of the Y and the Z model within the imputation process. It turns out that failure scenarios can be distinguished by comparing the CIA and the IVA in the completely observed dataset.
Finally, both approaches to statistical matching, i.e. the classical approach and the integrated approach, are subject to an extensive comparison in (1) a model-based simulation study and (2) a simulation study based on the AMELIA dataset, which is an openly available very large synthetic dataset and, by construction, similar to the EU-SILC survey. As an additional integrated approach, a Bayesian additive regression trees (BART) model is considered for modelling Y. These integrated procedures are compared to the classical approach represented by predictive mean matching in the form of multiple imputations by chained equation. Suitably chosen, the first simulation framework offers the possibility to clarify aspects related to the underlying assumptions by comparing the IVA and the CIA and by evaluating the impact of the matching variables. Thus, within this simulation study two related aspects are of special interest: the assumptions underlying each method and the incorporation of additional matching variables. The simulation on the AMELIA dataset offers a close-to-reality framework with the advantage of knowing the whole setting, i.e. the whole data X, Y and Z. Special interest lies in investigating assumptions through adding and excluding auxiliary variables in order to enhance conditional independence and assess the sensitivity of the methods to this issue. Furthermore, the benefit of having an overlap of units in data A and B for which information on X, Y, Z is available is investigated. It turns out that the integrated approach yields better results than the classical approach when the CIA clearly does not hold. Moreover, even when the classical approach obtains unbiased results for the regression coefficient of Y in the model for Z, it is the method relying on BART that over all coefficients performs best.
Concluding, this work constitutes a major contribution to the clarification of assumptions essential to any statistical matching procedure. By introducing graphical models to identify existing approaches to statistical matching combined with the subsequent analysis of the matched dataset, it offers an extensive overview, categorisation and extension of theory and application. Furthermore, in a setting where none of the assumptions are testable (since X, Y and Z are not observed together), the integrated approach is a valuable asset by offering an alternative to the CIA.
Mankind has dramatically influenced the nitrogen (N) fluxes between soil, vegetation, water and atmosphere " the global N cycle. Increasing intensification of agricultural land use, caused by the growing demand for agricultural products, has had major impacts on ecosystems worldwide. Particularly nitrogenous gases such as ammonia (NH3) have increased mainly due to industrial livestock farming. Countries with high N deposition rates require a variety of deposition measurements and effective N monitoring networks to assess N loads. Due to high costs, current "conventional"-deposition measurement stations are not widespread and therefore provide only a patchy picture of the real extent of the prevailing N deposition status over large areas. One tool that allows quantification of the exposure and the effects of atmospheric N impacts on an ecosystem is the use of bioindicators. Due to their specific physiology and ecology, especially lichens and mosses are suitable to reflect the atmospheric N input at ecosystem level. The present doctoral project began by investigating the general ability of epiphytic lichens to qualify and quantify N deposition by analysing both lichens and total N and δ15N along a gradient of different N emission sources and severity. The results showed that this was a viable monitoring method, and a grid-based monitoring system with nitrophytic lichens was set up in the western part of Germany. Finally, a critical appraisal of three different monitoring techniques (lichens, mosses and tree bark) was carried out to compare them with national relevant N deposition assessment programmes. In total 1057 lichen samples, 348 tree bark samples, 153 moss samples and 24 deposition water samples, were analysed in this dissertation at different investigation scales in Germany.The study identified species-specific ability and tolerance of various epiphytic lichens to accumulate N. Samples of tree bark were also collected and N accumulation ability was detected in connection with the increased intensity of agriculture, and according to the presence of reduced N compounds (NHx) in the atmosphere. Nitrophytic lichens (Xanthoria parietina, Physcia spp.) have the strongest correlations with high agriculture-related N deposition. In addition, the main N sources were revealed with the help of δ15N values along a gradient of altitude and areas affected by different types of land use (NH3 density classes, livestock units and various deposition types). Furthermore, in the first nationwide survey of Germany to compare lichens, mosses and tree bark samples as biomonitors for N deposition, it was revealed that lichens are clearly the most meaningful monitor organisms in highly N affected regions. Additionally, the study shows that dealing with different biomonitors is a difficult task due to their variety of N responses. The specific receptor surfaces of the indicators and therefore their different strategies of N uptake are responsible for the tissue N concentration of each organism group. It was also shown that the δ15N values depend on their N origin and the specific N transformations in each organism system, so that a direct comparison between atmosphere and ecosystems is not possible.In conclusion, biomonitors, and especially epiphytic lichens may serve as possible alternatives to get a spatially representative picture of the N deposition conditions. Furthermore, bioindication with lichens is a cost-efficient alternative to physico-chemical measurements to comprehensively assess different prevailing N doses and sources of N pools on a regional scale. They can at least support on-site deposition instruments by qualification and quantification of N deposition.
Time series archives of remotely sensed data offer many possibilities to observe and analyse dynamic environmental processes at the Earth- surface. Based on these hypertemporal archives, which offer continuous observations of vegetation indices, typically at repetition rates from one to two weeks, sets of phenological parameters or metrics can be derived. Examples of such parameters are the beginning and end of the annual growing period, as well as its length. Even though these parameters do not correspond exactly to conventional observations of phenological events, they nevertheless provide indications of the dynamic processes occurring in the biosphere. The development of robust algorithms for the derivation of phenological metrics can be challenging. Currently, such algorithms are most commonly based on digital filters or the Fourier analysis of time series. Polynomial spline models offer a useful alternative to existing methods. The possibilities of using spline models in the analytical description of time series are numerous, and their specific mathematical properties may help to avoid known problems occurring with the more common methods for deriving phenological metrics. Based on a selection of different polynomial spline models suitable for the analysis of remotely sensed time series of vegetation indices, a method to derive various phenological parameters from such time series was developed and implemented in this work. Using an example data set from an intensively used agricultural area showing highly dynamic variations in vegetation phenology, the newly developed method was verified by a comparison of the results of the spline based approach to the results of two alternative, well established methods.
The subject of this thesis is a homological approach to the splitting theory of PLS-spaces, i.e. to the question for which topologically exact short sequences 0->X->Y->Z->0 of PLS-spaces X,Y,Z the right-hand map admits a right inverse. We show that the category (PLS) of PLS-spaces and continuous linear maps is an additive category in which every morphism admits a kernel and a cokernel, i.e. it is pre-abelian. However, we also show that it is neither quasi-abelian nor semi-abelian. As a foundation for our homological constructions we show the more general result that every pre-abelian category admits a largest exact structure in the sense of Quillen. In the pre-abelian category (PLS) this exact structure consists precisely of the topologically exact short sequences of PLS-spaces. Using a construction of Ext-functors due to Yoneda, we show that one can define for each PLS-space A and every natural number k the k-th abelian-group valued covariant and contravariant Ext-functors acting on the category (PLS) of PLS-spaces, which induce for every topologically exact short sequence of PLS-spaces a long exact sequence of abelian groups and group morphisms. These functors are studied in detail and we establish a connection between the Ext-functors of PLS-spaces and the Ext-functors for LS-spaces. Through this connection we arrive at an analogue of a result for Fréchet spaces which connects the first derived functor of the projective limit with the first Ext-functor and also gives sufficient conditions for the vanishing of the higher Ext-functors. Finally, we show that Ext^k(E,F) = 0 for a k greater or equal than 1, whenever E is a closed subspace and F is a Hausdorff-quotient of the space of distributions, which generalizes a result of Wengenroth that is itself a generalization of results due to Domanski and Vogt.
The goal of this thesis is to transfer the logarithmic barrier approach, which led to very efficient interior-point methods for convex optimization problems in recent years, to convex semi-infinite programming problems. Based on a reformulation of the constraints into a nondifferentiable form this can be directly done for convex semi- infinite programming problems with nonempty compact sets of optimal solutions. But, by means of an involved max-term this reformulation leads to nondifferentiable barrier problems which can be solved with an extension of a bundle method of Kiwiel. This extension allows to deal with inexact objective values and subgradient information which occur due to the inexact evaluation of the maxima. Nevertheless we are able to prove similar convergence results as for the logarithmic barrier approach in the finite optimization. In the further course of the thesis the logarithmic barrier approach is coupled with the proximal point regularization technique in order to solve ill-posed convex semi-infinite programming problems too. Moreover this coupled algorithm generates sequences converging to an optimal solution of the given semi-infinite problem whereas the pure logarithmic barrier only produces sequences whose accumulation points are such optimal solutions. If there are certain additional conditions fulfilled we are further able to prove convergence rate results up to linear convergence of the iterates. Finally, besides hints for the implementation of the methods we present numerous numerical results for model examples as well as applications in finance and digital filter design.
A matrix A is called completely positive if there exists an entrywise nonnegative matrix B such that A = BB^T. These matrices can be used to obtain convex reformulations of for example nonconvex quadratic or combinatorial problems. One of the main problems with completely positive matrices is checking whether a given matrix is completely positive. This is known to be NP-hard in general. rnrnFor a given matrix completely positive matrix A, it is nontrivial to find a cp-factorization A=BB^T with nonnegative B since this factorization would provide a certificate for the matrix to be completely positive. But this factorization is not only important for the membership to the completely positive cone, it can also be used to recover the solution of the underlying quadratic or combinatorial problem. In addition, it is not a priori known how many columns are necessary to generate a cp-factorization for the given matrix. The minimal possible number of columns is called the cp-rank of A and so far it is still an open question how to derive the cp-rank for a given matrix. Some facts on completely positive matrices and the cp-rank will be given in Chapter 2. Moreover, in Chapter 6, we will see a factorization algorithm, which, for a given completely positive matrix A and a suitable starting point, computes the nonnegative factorization A=BB^T. The algorithm therefore returns a certificate for the matrix to be completely positive. As introduced in Chapter 3, the fundamental idea of the factorization algorithm is to start from an initial square factorization which is not necessarily entrywise nonnegative, and extend this factorization to a matrix for which the number of columns is greater than or equal to the cp-rank of A. Then it is the goal to transform this generated factorization into a cp-factorization. This problem can be formulated as a nonconvex feasibility problem, as shown in Section 4.1, and solved by a method which is based on alternating projections, as proven in Chapter 6. On the topic of alternating projections, a survey will be given in Chapter 5. Here we will see how to apply this technique to several types of sets like subspaces, convex sets, manifolds and semialgebraic sets. Furthermore, we will see some known facts on the convergence rate for alternating projections between these types of sets. Considering more than two sets yields the so called cyclic projections approach. Here some known facts for subspaces and convex sets will be shown. Moreover, we will see a new convergence result on cyclic projections among a sequence of manifolds in Section 5.4. In the context of cp-factorizations, a local convergence result for the introduced algorithm will be given. This result is based on the known convergence for alternating projections between semialgebraic sets. To obtain cp-facrorizations with this first method, it is necessary to solve a second order cone problem in every projection step, which is very costly. Therefore, in Section 6.2, we will see an additional heuristic extension, which improves the numerical performance of the algorithm. Extensive numerical tests in Chapter 7 will show that the factorization method is very fast in most instances. In addition, we will see how to derive a certificate for the matrix to be an element of the interior of the completely positive cone. As a further application, this method can be extended to find a symmetric nonnegative matrix factorization, where we consider an additional low-rank constraint. Here again, the method to derive factorizations for completely positive matrices can be used, albeit with some further adjustments, introduced in Section 8.1. Moreover, we will see that even for the general case of deriving a nonnegative matrix factorization for a given rectangular matrix A, the key aspects of the completely positive factorization approach can be used. To this end, it becomes necessary to extend the idea of finding a completely positive factorization such that it can be used for rectangular matrices. This yields an applicable algorithm for nonnegative matrix factorization in Section 8.2. Numerical results for this approach will suggest that the presented algorithms and techniques to obtain completely positive matrix factorizations can be extended to general nonnegative factorization problems.
Die Dissertation beschäftigt sich mit einer neuartigen Art von Branch-and-Bound Algorithmen, deren Unterschied zu klassischen Branch-and-Bound Algorithmen darin besteht, dass
das Branching durch die Addition von nicht-negativen Straftermen zur Zielfunktion erfolgt
anstatt durch das Hinzufügen weiterer Nebenbedingungen. Die Arbeit zeigt die theoretische Korrektheit des Algorithmusprinzips für verschiedene allgemeine Klassen von Problemen und evaluiert die Methode für verschiedene konkrete Problemklassen. Für diese Problemklassen, genauer Monotone und Nicht-Monotone Gemischtganzzahlige Lineare Komplementaritätsprobleme und Gemischtganzzahlige Lineare Probleme, präsentiert die Arbeit
verschiedene problemspezifische Verbesserungsmöglichkeiten und evaluiert diese numerisch.
Weiterhin vergleicht die Arbeit die neue Methode mit verschiedenen Benchmark-Methoden
mit größtenteils guten Ergebnissen und gibt einen Ausblick auf weitere Anwendungsgebiete
und zu beantwortende Forschungsfragen.
Two areas were selected to represent major process regimes of Mediterranean rangelands. In the County of Lagads (Greece), situated east of the city of Thessaloniki, livestock grazing with sheep and goats is a major factor of the rural economy. In suitable areas, it is complemented by agricultural use. The region of Ayora (Spain) is located west of the city of Valencia. It is one of regions most affected by fires in Spain. First of all, long time series of satellite data were compiled for both regions on the basis of Landsat sensors, which cover the time until 1976 (Ayora) and 1984 (Lagadas) with one image per year. Using a rigorous processing scheme, the data were geometrically and radiometrically corrected Specific attention was given to an exact sensor calibration, the radiometric intercalibration of Landsat-TM and "MSS. Proportional cover of photosynthetically active vegetation was identified as a suitable quantitative indicator for assessing the state of rangelands. Using Spectral Mixture Analysis (SMA) it was inferred for all data sets. The extensive data base procured this way enabled to map fire events in the Ayora area based on sequential diachronic sets and provide fire dates, perimeter as well as fire recurrence for each pixel. The increasing fire frequency in the past decades is in large parts attributed to the accelerated abandonment of the area that leads to an encroachment of shrublands and the accumulation of combustible biomass. On the basis of the fire mapping results, a spatial and temporal stratification of the data set allowed to asses plant recovery dynamics on the landscape level through linear trend analysis. The long history of fire events in the Mediterranean frequently leads to processes of auto-succession. Following an initial dominance of herbaceous vegetation this commonly leads to similar plant communities as the ones present before the fire. On a temporal axis, this results in typical exponential post-fire trajectories which could also be shown in this study. The analysis of driving factors for post-fire dynamics confirmed the importance of aspect and slope. Locations with lower amounts of solar irradiation and favourable water supply yielded faster recovery rates and higher post-fire vegetation cover levels. In most cases, the vegetation cover levels observed before the fire were not reached within the post-fire observation period. In the area of Lagadas, linear trend analysis and additional statistical parameters were used to infer a degradation index. This could be used to illustrate a complex pattern of stability, regeneration and degradation of vegetation cover. These different processes and states are found in close proximity and are clearly determined by topography and elevation. Following a sequence of analyses, it was found that in particular steep, narrow valleys show positive trends, while negative trends are more abundant on plain or gently undulating areas. Considering the local grazing regime, this spatial differentiation was related to the accessibility of specific locations. Subsequently, animal numbers on community level were used to calculate efficient stocking rates and assess the temporal development of their relation with vegetation cover. This calculation of temporal trajectories illustrated that only some communities show the expected negative relation. To the contrary, a positive relation or even changing relation patterns are observed. This signifies recent concentration and intensification processes in the grazing scheme, as a result of which animals are kept in sheds, where additional feedstuffs are provided. In these cases, free roaming of livestock animals is often confined to some hours every day, which explains the spatial preference of easily accessible areas by the shepherds. Beyond these temporal trends, it was analysed whether the grazing pattern is equally reflected in a spatial trend. Making use of available geospatial information layers, the efforts required to reach each location was expressed as a cost. Then, cost zones could be defined and woody vegetation cover as a grazing indicator could be inferred for the different zones. Animal sheds were employed as starting features for this piospheric analysis, which could be mapped from very high spatial resolution Quickbird image data. The result was a clearly structured gradient showing increasing woody vegetation cover with increasing cost distance. On the basis of these two pilot studies, the elements of a monitoring and interpretation framework identified at the beginning of the work were evaluated and a formal interpretation scheme was presented.
The following dissertation contains three studies examining academic boredom development in five high-track German secondary schools (AVG-project data; Study 1: N = 1,432; Study 2: N = 1,861; Study 3: N = 1,428). The investigation period spanned 3.5 years, with four waves of measurement from grades 5 to 8 (T1: 5th grade, after transition to secondary school; T2: 5th grade, after mid-term evaluations; T3: 6th grade, after mid-term evaluations; T4: 8th grade, after mid-term evaluations). All three studies featured cross-sectional and longitudinal analyses, separating, and comparing the subject domains of mathematics and German.
Study 1 provided an investigation of academic boredom’s factorial structure alongside correlational and reciprocal relations of different forms of boredom and academic self-concept. Analyses included reciprocal effects models and latent correlation analyses. Results indicated separability of boredom intensity, boredom due to underchallenge and boredom due to overchallenge, as separate, correlated factors. Evidence for reciprocal relations between boredom and academic self-concept was limited.
Study 2 examined the effectiveness and efficacy of full-time ability grouping for as a boredom intervention directed at the intellectually gifted. Analyses included propensity score matching, and latent growth curve modelling. Results pointed to limited effectiveness and efficacy for full-time ability grouping regarding boredom reduction.
Study 3 explored gender differences in academic boredom development, mediated by academic interest, academic self-concept, and previous academic achievement. Analyses included measurement invariance testing, and multiple-indicator-multi-cause-models. Results showed one-sided gender differences, with boys reporting less favorable boredom development compared to girls, even beyond the inclusion of relevant mediators.
Findings from all three studies were embedded into the theoretical framework of control-value theory (Pekrun, 2006; 2019; Pekrun et al., 2023). Limitations, directions for future research, and practical implications were acknowledged and discussed.
Overall, this dissertation yielded important insights into boredom’s conceptual complexity. This concerned factorial structure, developmental trajectories, interrelations to other learning variables, individual differences, and domain specificities.
Keywords: Academic boredom, boredom intensity, boredom due to underchallenge, boredom due to overchallenge, ability grouping, gender differences, longitudinal data analysis, control-value theory