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This study focuses on the representation of British South Asian identities in contemporary British audiovisual media. It attempts to answer the question, whether these identities are represented as hybrid, heterogeneous and ambivalent, or whether these contemporary representations follow in the tradition of colonial and postcolonial racialism. Racialised depictions of British South Asians have been the norm not only in the colonial but also in the postcolonial era until the rise of the Black British movement, whose successes have been also acknowledged in the field of representation. However these achievements have to be scrutinized again, especially in the context of the post 9/11 world, rising Islamophobia, and new forms of institutionalized discrimination on the basis of religion. Since the majority of British Muslims are of South Asian origin, this study tries to answer the question whether the marker of religious origin is racial belonging, i.e. skin colour, and old stereotypes associated with the racialised representation are being perpetuated into current depictions through an examination of the varied genre of popular audio visual media texts.

The main topic of this treatise is the solution of two problems from the general theory of linear partial differential equations with constant coefficients. While surjectivity criteria for linear partial differential operators in spaces of smooth functions over an open subset of euclidean space and distributions were proved by B. Malgrange and L. Hörmander in 1955, respectively 1962, concrete evaluation of these criteria is still a highly non-trivial task. In particular, it is well-known that surjectivity in the space of smooth functions over an open subset of euclidean space does not automatically imply surjectivity in the space of distributions. Though, examples for this fact all live in three or higher dimensions. In 1966, F. Trèves conjectured that in the two dimensional setting surjectivity of a linear partial differential operator on the smooth functions indeed implies surjectivity on the space of distributions. An affirmative solution to this problem is presented in this treatise. The second main result solves the so-called problem of (distributional) parameter dependence for solutions of linear partial differential equations with constant coefficients posed by J. Bonet and P. Domanski in 2006. It is shown that, in dimensions three or higher, this problem in general has a negative solution even for hypoelliptic operators. Moreover, it is proved that the two dimensional case is again an exception, because in this setting the problem of parameter dependence always has a positive solution.

Magnet Resonance Imaging (MRI) and Electroencephalography (EEG) are tools used to investigate the functioning of the working brain in both humans and animal studies. Both methods are increasingly combined in separate or simultaneous measurements under the assumption to benefit from their individual strength while compensating their particular weaknesses. However, little attention has been paid to how statistical analyses strategies can influence the information that can be retrieved from a combined EEG fMRI study. Two independent studies in healthy student volunteers were conducted in the context of emotion research to demonstrate two approaches of combining MRI and EEG data of the same participants. The first study (N = 20) applied a visual search paradigm and found that in both measurements the assumed effects were absent by not statistically combining their results. The second study (N = 12) applied a novelty P300 paradigm and found that only the statistical combination of MRI and EEG measurements was able to disentangle the functional effects of brain areas involved in emotion processing. In conclusion, the observed results demonstrate that there are added benefits of statistically combining EEG-fMRI data acquisitions by assessing both the inferential statistical structure and the intra-individual correlations of the EEG and fMRI signal.

One of the main tasks in mathematics is to answer the question whether an equation possesses a solution or not. In the 1940- Thom and Glaeser studied a new type of equations that are given by the composition of functions. They raised the following question: For which functions Î¨ does the equation F(Î¨)=f always have a solution. Of course this question only makes sense if the right hand side f satisfies some a priori conditions like being contained in the closure of the space of all compositions with Î¨ and is easy to answer if F and f are continuous functions. Considering further restrictions to these functions, especially to F, extremely complicates the search for an adequate solution. For smooth functions one can already find deep results by Bierstone and Milman which answer the question in the case of a real-analytic function Î¨. This work contains further results for a different class of functions, namely those Î¨ that are smooth and injective. In the case of a function Î¨ of a single real variable, the question can be fully answered and we give three conditions that are both sufficient and necessary in order for the composition equation to always have a solution. Furthermore one can unify these three conditions to show that they are equivalent to the fact that Î¨ has a locally Hölder-continuous inverse. For injective functions Î¨ of several real variables we give necessary conditions for the composition equation to be solvable. For instance Î¨ should satisfy some form of local distance estimate for the partial derivatives. Under the additional assumption of the Whitney-regularity of the image of Î¨, we can give sufficient conditions for flat functions f on the critical set of Î¨ to possess a solution F(Î¨)=f.

Optimal control problems are optimization problems governed by ordinary or partial differential equations (PDEs). A general formulation is given byrn \min_{(y,u)} J(y,u) with subject to e(y,u)=0, assuming that e_y^{-1} exists and consists of the three main elements: 1. The cost functional J that models the purpose of the control on the system. 2. The definition of a control function u that represents the influence of the environment of the systems. 3. The set of differential equations e(y,u) modeling the controlled system, represented by the state function y:=y(u) which depends on u. These kind of problems are well investigated and arise in many fields of application, for example robot control, control of biological processes, test drive simulation and shape and topology optimization. In this thesis, an academic model problem of the form \min_{(y,u)} J(y,u):=\min_{(y,u)}\frac{1}{2}\|y-y_d\|^2_{L^2(\Omega)}+\frac{\alpha}{2}\|u\|^2_{L^2(\Omega)} subject to -\div(A\grad y)+cy=f+u in \Omega, y=0 on \partial\Omega and u\in U_{ad} is considered. The objective is tracking type with a given target function y_d and a regularization term with parameter \alpha. The control function u takes effect on the whole domain \Omega. The underlying partial differential equation is assumed to be uniformly elliptic. This problem belongs to the class of linear-quadratic elliptic control problems with distributed control. The existence and uniqueness of an optimal solution for problems of this type is well-known and in a first step, following the paradigm 'first optimize, then discretize', the necessary and sufficient optimality conditions are derived by means of the adjoint equation which ends in a characterization of the optimal solution in form of an optimality system. In a second step, the occurring differential operators are approximated by finite differences and the hence resulting discretized optimality system is solved with a collective smoothing multigrid method (CSMG). In general, there are several optimization methods for solving the optimal control problem: an application of the implicit function theorem leads to so-called black-box approaches where the PDE-constrained optimization problem is transformed into an unconstrained optimization problem and the reduced gradient for these reduced functional is computed via the adjoint approach. Another possibilities are Quasi-Newton methods, which approximate the Hessian by a low-rank update based on gradient evaluations, Krylov-Newton methods or (reduced) SQP methods. The use of multigrid methods for optimization purposes is motivated by its optimal computational complexity, i.e. the number of required computer iterations scales linearly with the number of unknowns and the rate of convergence, which is independent of the grid size. Originally multigrid methods are a class of algorithms for solving linear systems arising from the discretization of partial differential equations. The main part of this thesis is devoted to the investigation of the implementability and the efficiency of the CSMG on commodity graphics cards. GPUs (graphic processing units) are designed for highly parallelizable graphics computations and possess many cores of SIMD-architecture, which are able to outperform the CPU regarding to computational power and memory bandwidth. Here they are considered as prototype for prospective multi-core computers with several hundred of cores. When using GPUs as streamprocessors, two major problems arise: data have to be transferred from the CPU main memory to the GPU main memory, which can be quite slow and the limited size of the GPU main memory. Furthermore, only when the streamprocessors are fully used to capacity, a remarkable speed-up comparing to a CPU is achieved. Therefore, new algorithms for the solution of optimal control problems are designed in this thesis. To this end, a nonoverlapping domain decomposition method is introduced which allows the exploitation of the computational power of many GPUs resp. CPUs in parallel. This algorithm is based on preliminary work for elliptic problems and enhanced for the application to optimal control problems. For the domain decomposition into two subdomains the linear system for the unknowns on the interface is solved with a Schur complement method by using a discrete approximation of the Steklov-Poincare operator. For the academic optimal control problem, the arising capacitance matrix can be inverted analytically. On this basis, two different algorithms for the nonoverlapping domain decomposition for the case of many subdomains are proposed in this thesis: on the one hand, a recursive approach and on the other hand a simultaneous approach. Numerical test compare the performance of the CSMG for the one domain case and the two approaches for the multi-domain case on a GPU and CPU for different variants.

In this thesis, in order to shed light on the biological function of the membrane-bound Glucocorticoid Receptor (mGR), proteomic changes induced by 15 min in vivo acute stress and by short in vitro activation of the mGR were analyzed in T-lymphocytes. The numerous overlaps between the two datasets suggest that the mGR mediates physiologically relevant actions and participates in the early stress response, triggering rapid early priming events that pave the way for the slower genomic GC activities. In addition, a new commercially available method with suitable sensitivity to detect the human mGR is reported and the transcriptional origin of this protein investigated. Our results indicates that specific GR-transcripts, containing exon 1C and 1D, are associated with the expression of this membrane isoform.

The contribution of three genes (C15orf53, OXTR and MLC1) to the etiology of chromosome 15-bound schizophrenia (SCZD10), bipolar disorder (BD) and autism spectrum disorder (ASD) were studied. At first, the uncharacterized gene C15orf53 was comprehensively analyzed. Previous genome-wide association studies (GWAS) in bipolar disorder samples have identified an association signal in close vicinity to C15orf53 on chromosome 15q14. This gene is located in exactly the genomic region, which is segregating in our SCZD10 families. An association study with bipolar disorder (BD) and SCZD10 individual samples did not reveal any association of single nucleotide polymorphisms (SNPs) in C15orf53. Mutational analysis of C15orf53 in SCZD10-affected individuals from seven multiplex families did not show any mutations in the 5'-untranslated region, the coding region and the intron-exon boundaries. Gene expression analysis revealed that C15orf53 was expressed in a subpopulation of leukocytes, but not in human post-mortem limbic brain tissue. Summarizing these studies, C15orf53 is unlikely to be a strong candidate gene for the etiology of BD or SCZD10. The second investigated gene was the human oxytocin receptor gene (OXTR). Five well described SNPs located in the OXTR gene were taken for a transmission-disequilibrium test (TDT) in parents-child trios with ASD-affected children. Neither in the complete sample nor in a subgroup with children that had an intelligence quotient (IQ) above 70, association was found, independent from the application of Haploview or UNPHASED for analysis. The third gene, MLC1, was investigated with regards to its implication in the etiology of SCZD10. Mutations in the MLC1 gene lead to megalencephalic leukoencephalopathy with subcortical cysts (MLC) and one variant coding for the amino acid methionine (Met) instead of leucine (Leu) at position 309 was identified to segregate in a family affected with SCZD10. For further investigation of MLC1 and its possible implication in the etiology of SCZD10, a constitutive Mlc1 knockout mouse model should be created. Mouse embryonic stem cells (mES) were electroporated with a knockout vector construct and analyzed with respect to homologous recombination of the knockout construct with the genomic DNA (gDNA) of the mES. Polymerase chain reaction (PCR) on the available stem cell clones did not reveal any homologous recombined ES. Additionally, we conducted experiments to knockdown MLC1 and using microRNAs. The 3'-untranslated region of the MLC1 gene was analyzed with the bioinformatics tool TargetScan to screen for potential microRNA target sites. In the 3'-untranslated region of the MLC1 gene, a potential binding site for miR-137 was identified. The gene expression level of genes that had been linked to psychiatric disorders and carried a predicated miR-137 binding site has been proven to be immediately responsive to miR-137. Thus, there is new evidence that MLC1 is a candidate gene for the etiology of SCZD10.

The stress hormone cortisol as the end-product of the hypothalamic-pituitary-adrenal (HPA) axis has been found to play a crucial role in the release of aggressive behavior (Kruk et al., 2004; Böhnke et al., 2010). In order to further explore potential mechanisms underlying the relationship between stress and aggression, such as changes in (social) information processing, we conducted two experimental studies that are presented in this thesis. In both studies, acute stress was induced by means of the Socially Evaluated Cold Pressor Test (SECP) designed by Schwabe et al. (2008). Stressed participants were classified as either cortisol responders or nonresponders depending on their rise in cortisol following the stressor. Moreover, basal HPA axis activity was measured prior to the experimental sessions and EEG was recorded throughout the experiments. The first study dealt with the influence of acute stress on cognitive control processes. 41 healthy male participants were assigned to either the stress condition or the non-stressful control procedure of the SECP. Before as well as after the stress induction, all participants performed a cued task-switching paradigm in order to measure cognitive control processes. Results revealed a significant influence of acute and basal cortisol levels, respectively, on the motor preparation of the upcoming behavioral response, that was reflected in changes in the magnitude of the terminal Contingent Negative Variation (CNV). In the second study, the effect of acute stress and subsequent social provocation on approach-avoidance motivation was examined. 72 healthy students (36 males, 36 females) took part in the study. They performed an approach-avoidance task, using emotional facial expressions as stimuli, before as well as after the experimental manipulation of acute stress (again via the SECP) and social provocation realized by means of the Taylor Aggression Paradigm (Taylor, 1967). Additionally to salivary cortisol, testosterone samples were collected at several points in time during the experimental session. Results indicated a positive relationship between acute testosterone levels and the motivation to approach social threat stimuli in highly provoked cortisol responders. Similar results were found when the testosterone-to-cortisol ratio at baseline was taken into account instead of acute testosterone levels. Moreover, brain activity during the approach-avoidance task was significantly influenced by acute stress and social provocation, as reflected in reductions of early (P2) as well as of later (P3) ERP components in highly provoked cortisol responders. This may indicate a less accurate, rapid processing of socially relevant stimuli due to an acute increase in cortisol and subsequent social provocation. In conclusion, the two studies presented in this thesis provide evidence for significant changes in information processing due to acute stress, basal cortisol levels and social provocation, suggesting an enhanced preparation for a rapid behavioral response in the sense of a fight-or-flight reaction. These results confirm the model of Kruk et al. (2004) proposing a mediating role of changed information processes in the stress-aggression-link.

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.

Arctic and Antarctic polynya systems are of high research interest since extensive new ice formation takes place in these regions. The monitoring of polynyas and the ice production is crucial with respect to the changing sea-ice regime. The thin-ice thickness (TIT) distribution within polynyas controls the amount of heat that is released to the atmosphere and has therefore an impact on the ice-production rates. This thesis presents an improved method to retrieve thermal-infrared thin-ice thickness distributions within polynyas. TIT with a spatial resolution of 1 km Ã— 1 km is calculated using the MODIS ice-surface temperature and atmospheric model variables within the Laptev Sea polynya for the winter periods 2007/08 and 2008/09. The improvement of the algorithm is focused on the surface-energy flux parameterizations. Furthermore, a thorough sensitivity analysis is applied to quantify the uncertainty in the thin-ice thickness results. An absolute mean uncertainty of -±4.7 cm for ice below 20 cm of thickness is calculated. Furthermore, advantages and drawbacks using different atmospheric data sets are investigated. Daily MODIS TIT composites are computed to fill the data gaps arising from clouds and shortwave radiation. The resulting maps cover on average 70 % of the Laptev Sea polynya. An intercomparison of MODIS and AMSR-E polynya data indicates that the spatial resolution issue is essential for accurately deriving polynya characteristics. Monthly fast-ice masks are generated using the daily TIT composites. These fast-ice masks are implemented into the coupled sea-ice/ocean model FESOM. An evaluation of FESOM sea-ice concentrations is performed with the result that a prescribed high-resolution fast-ice mask is necessary regarding the accurate polynya location. However, for a more realistic simulation of other small-scale sea-ice features further model improvements are required. The retrieval of daily high-resolution MODIS TIT composites is an important step towards a more precise monitoring of thin sea ice and sea-ice production. Future work will address a combined remote sensing " model assimilation method to simulate fully-covered thin-ice thickness maps that enable the retrieval of accurate ice production values.