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Many NP-hard optimization problems that originate from classical graph theory, such as the maximum stable set problem and the maximum clique problem, have been extensively studied over the past decades and involve the choice of a subset of edges or vertices. There usually exist combinatorial methods that can be applied to solve them directly in the graph.
The most simple method is to enumerate feasible solutions and select the best. It is not surprising that this method is very slow oftentimes, so the task is to cleverly discard fruitless search space during the search. An alternative method to solve graph problems is to formulate integer linear programs, such that their solution yields an optimal solution to the original optimization problem in the graph. In order to solve integer linear programs, one can start with relaxing the integer constraints and then try to find inequalities for cutting off fractional extreme points. In the best case, it would be possible to describe the convex hull of the feasible region of the integer linear program with a set of inequalities. In general, giving a complete description of this convex hull is out of reach, even if it has a polynomial number of facets. Thus, one tries to strengthen the (weak) relaxation of the integer linear program best possible via strong inequalities that are valid for the convex hull of feasible integer points.
Many classes of valid inequalities are of exponential size. For instance, a graph can have exponentially many odd cycles in general and therefore the number of odd cycle inequalities for the maximum stable set problem is exponential. It is sometimes possible to check in polynomial time if some given point violates any of the exponentially many inequalities. This is indeed the case for the odd cycle inequalities for the maximum stable set problem. If a polynomial time separation algorithm is known, there exists a formulation of polynomial size that contains a given point if and only if it does not violate one of the (potentially exponentially many) inequalities. This thesis can be divided into two parts. The first part is the main part and it contains various new results. We present new extended formulations for several optimization problems, i.e. the maximum stable set problem, the nonconvex quadratic program with box
constraints and the p-median problem. In the second part we modify a very fast algorithm for finding a maximum clique in very large sparse graphs. We suggest and compare three alternative versions of this algorithm to the original version and compare their strengths and weaknesses.
No Longer Printing the Legend: The Aporia of Heteronormativity in the American Western (1903-1969)
(2023)
This study critically investigates the U.S.-American Western and its construction of sexuality and gender, revealing that the heteronormative matrix that is upheld and defended in the genre is consistently preceded by the exploration of alternative sexualities and ways to think gender beyond the binary. The endeavor to naturalize heterosexuality seems to be baked in the formula of the U.S.-Western. However, as I show in this study, this endeavor relies on an aporia, because the U.S.-Western can only ever attempt to naturalize gender by constructing it first, hence inevitably and simultaneously construct evidence that supports the opposite: the unnaturalness and contingency of gender and sexuality.
My study relies on the works of Raewyn Connell, Pierre Bourdieu, and Judith Butler, and amalgamates in its methodology established approaches from film and literary studies (i.e., close readings) with a Foucaultian understanding of discourse and discourse analysis, which allows me to relate individual texts to cultural, socio-political and economical contexts that invariably informed the production and reception of any filmic text. In an analysis of 14 U.S.-Westerns (excluding three excursions) that appeared between 1903 and 1969 I give ample and minute narrative and film-aesthetical evidence to reveal the complex and contradictory construction of gender and sexuality in the U.S.-Western, aiming to reveal both the normative power of those categories and its structural instability and inconsistency.
This study proofs that the Western up until 1969 did not find a stable pattern to represent the gender binary. The U.S.-Western is not necessarily always looking to confirm or stabilize governing constructs of (gendered) power. However, it without fail explores and negotiates its legitimacy. Heterosexuality and male hegemony are never natural, self-evident, incontestable, or preordained. Quite conversely: the U.S.-Western repeatedly – and in a surprisingly diverse and versatile way – reveals the illogical constructedness of the heteronormative matrix.
My study therefore offers a fresh perspective on the genre and shows that the critical exploration and negotiation of the legitimacy of heteronormativity as a way to organize society is constitutive for the U.S.-Western. It is the inquiry – not necessarily the affirmation – of the legitimacy of this model that gives the U.S.-Western its ideological currency and significance as an artifact of U.S.-American popular culture.
Nonlocal operators are used in a wide variety of models and applications due to many natural phenomena being driven by nonlocal dynamics. Nonlocal operators are integral operators allowing for interactions between two distinct points in space. The nonlocal models investigated in this thesis involve kernels that are assumed to have a finite range of nonlocal interactions. Kernels of this type are used in nonlocal elasticity and convection-diffusion models as well as finance and image analysis. Also within the mathematical theory they arouse great interest, as they are asymptotically related to fractional and classical differential equations.
The results in this thesis can be grouped according to the following three aspects: modeling and analysis, discretization and optimization.
Mathematical models demonstrate their true usefulness when put into numerical practice. For computational purposes, it is important that the support of the kernel is clearly determined. Therefore nonlocal interactions are typically assumed to occur within an Euclidean ball of finite radius. In this thesis we consider more general interaction sets including norm induced balls as special cases and extend established results about well-posedness and asymptotic limits.
The discretization of integral equations is a challenging endeavor. Especially kernels which are truncated by Euclidean balls require carefully designed quadrature rules for the implementation of efficient finite element codes. In this thesis we investigate the computational benefits of polyhedral interaction sets as well as geometrically approximated interaction sets. In addition to that we outline the computational advantages of sufficiently structured problem settings.
Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve interface-dependent kernels. We derive the shape derivative associated to the nonlocal system model and solve the problem by established numerical techniques.
In this psycho-neuro-endocrine study the molecular basis of different variants of steroid receptors as well as highly conserved non steroidal receptors was investigated. These nuclear receptors (NRs) are important key regulators of a wide variety of different physiological and pathophysiological challenges ranging from inflammation and stress to complex behaviour and disease. NRs control gene transcription in a ligand dependent manner and are embedded in the huge interaction network of the neuroendocrine and immune system. Two receptors, the glucocorticoid receptor (GR) and the chicken ovalbumin upstream promoter-transcription factorII (Coup-TFII), both expressed in the immune and nervous system, were investigated regarding possible splice variants and their implication in the control of gene transcription. Both NRs are known to interact and modulate each other- target gene regulation. This study could be shown that both NRs have different splice variants that are expressed in a tissue specific manner. The different 5-´alternative transcript variants of the human GR were in silico identified in other species and evidence for a highly conserved and tightly controlled function was provided. Investigations of the N-terminal transactivation domain of the GR showed a deletion suggesting an altered glucocorticoid-dependent transactivation profile. The newly identified alternative transcript variant of Coup-TFII leads to a DNA binding deficient Coup-TFII isoform that is highly expressed in the brain. This Coup-TFII isoform alters Coup-TFII target gene expression and is suggested to interact with GR via its ligand binding domain resulting in an impaired GR target gene regulation in the nervous system. In this thesis it was demonstrated that NR variants are important for the understanding of the enormous regulatory potential of this receptor family and have to be taken into account for the development of therapeutic strategies for complex diseases such as stress related and neurodegenerative disorders.
In this thesis, we present a new approach for estimating the effects of wind turbines for a local bat population. We build an individual based model (IBM) which simulates the movement behaviour of every single bat of the population with its own preferences, foraging behaviour and other species characteristics. This behaviour is normalized by a Monte-Carlo simulation which gives us the average behaviour of the population. The result is an occurrence map of the considered habitat which tells us how often the bat and therefore the considered bat population frequent every region of this habitat. Hence, it is possible to estimate the crossing rate of the position of an existing or potential wind turbine. We compare this individual based approach with a partial differential equation based method. This second approach produces a lower computational effort but, unfortunately, we lose information about the movement trajectories at the same time. Additionally, the PDE based model only gives us a density profile. Hence, we lose the information how often each bat crosses special points in the habitat in one night. In a next step we predict the average number of fatalities for each wind turbine in the habitat, depending on the type of the wind turbine and the behaviour of the considered bat species. This gives us the extra mortality caused by the wind turbines for the local population. This value is used for a population model and finally we can calculate whether the population still grows or if there already is a decline in population size which leads to the extinction of the population. Using the combination of all these models, we are able to evaluate the conflict of wind turbines and bats and to predict the result of this conflict. Furthermore, it is possible to find better positions for wind turbines such that the local bat population has a better chance to survive. Since bats tend to move in swarm formations under certain circumstances, we introduce swarm simulation using partial integro-differential equations. Thereby, we have a closer look at existence and uniqueness properties of solutions.
Today obesity has been recognized as a disease. Evidence suggests that obesity often has Genetic, environmental, psychological and other factors. Growing evidence points to heredity as a strong determining factor of obesity. The characterization of uncoupling proteins (UCP) represents a major breakthrough of genetic factors towards understanding the molecular basis for energy expenditure and therefore likely to have important implication for the cause and treatment of human obesity. UCPs as mitochondrial anion carriers which creates a pathway that allows dissipation of the proton electrochemical gradient therefore which when deregulated are key risk factors in the development of obesity and other eating disorders. In order to better understand the roles of both UCP2 and UCP3 which considered as prime candidate genes involved in the pathogenesis of obesity, this study elucidate (1) Genomic organization: The human UCP2 (3) gene spans over 8.7 kb (7.5 kb) distributed on 8 (7) exons. Three UCP genes may have evolved from a common ancestor or are the result from gene duplication events. Two mRNA transcripts are generated from hUCP3 gene, the long and short form of hUCP3 is differing by the presence or absence of 37 amino acid residues at the C-terminus. (2) Mutational analysis revealed a mutation in exon 4 of hUCP2 resulting in the substitution of an alanine by a valine at codon 55 and an insertion polymorphism in exon 8 consisted of a 45 bp repeat located 150 bp downstream of the stop codon in the 3'-UTR. The allele frequencies of both polymorphisms were not significantly elevated in a subgroup of children characterized by low Resting Metabolic Rates (RMR). (3) Promoter Analysis showed that the promoter region of hUCP2 lacks a classical TATA or CAAT box. Functional characterization of hUCP2 promoter showed that minimal promoter activity was observed within 65 bp upstream of the transcriptional start site. 75 bp further upstream a strong cis-acting regulatory element was identified which significantly enhanced basal promoter activity. The regulation of human UCP2 gene expression involves complex interactions among positive and negative regulatory elements. the 5"-flanking region of the hUCP3 gene were characterized in which contains both TATA and CAAT boxes as well as consensus motifs for PPRE, TRE, CRE and muscle-specific MyoD and MEF2 sites. Functional characterization identified a cis-acting negative regulatory element between - 2983 and -982 while the region between -982 and -284 showed greatly increased basal promoter activity suggesting the presence of a strong enhancer element. Promoter activity was particularly enhanced in the murine skeletal muscle cell line C2C12 reflecting the tissue-selective expression pattern of UCP3.
The parameterization of ocean/sea-ice/atmosphere interaction processes is a challenge for regional climate models (RCMs) of the Arctic, particularly for wintertime conditions, when small fractions of thin ice or open water cause strong modifications of the boundary layer. Thus, the treatment of sea ice and sub-grid flux parameterizations in RCMs is of crucial importance. However, verification data sets over sea ice for wintertime conditions are rare. In the present paper, data of the ship-based experiment Transarktika 2019 during the end of the Arctic winter for thick one-year ice conditions are presented. The data are used for the verification of the regional climate model COSMO-CLM (CCLM). In addition, Moderate Resolution Imaging Spectroradiometer (MODIS) data are used for the comparison of ice surface temperature (IST) simulations of the CCLM sea ice model. CCLM is used in a forecast mode (nested in ERA5) for the Norwegian and Barents Seas with 5 km resolution and is run with different configurations of the sea ice model and sub-grid flux parameterizations. The use of a new set of parameterizations yields improved results for the comparisons with in-situ data. Comparisons with MODIS IST allow for a verification over large areas and show also a good performance of CCLM. The comparison with twice-daily radiosonde ascents during Transarktika 2019, hourly microwave water vapor measurements of first 5 km in the atmosphere and hourly temperature profiler data show a very good representation of the temperature, humidity and wind structure of the whole troposphere for CCLM.
In 2014/2015 a one-year field campaign at the Tiksi observatory in the Laptev Sea area was carried out using Sound Detection and Ranging/Radio Acoustic Sounding System (SODAR/RASS) measurements to investigate the atmospheric boundary layer (ABL) with a focus on low-level jets (LLJ) during the winter season. In addition to SODAR/RASS-derived vertical profiles of temperature, wind speed and direction, a suite of complementary measurements at the Tiksi observatory was available. Data of a regional atmospheric model were used to put the local data into the synoptic context. Two case studies of LLJ events are presented. The statistics of LLJs for six months show that in about 23% of all profiles LLJs were present with a mean jet speed and height of about 7 m/s and 240 m, respectively. In 3.4% of all profiles LLJs exceeding 10 m/s occurred. The main driving mechanism for LLJs seems to be the baroclinicity, since no inertial oscillations were found. LLJs with heights below 200 m are likely influenced by local topography.
The first part of this thesis offers a theoretical foundation for the analysis of Tolkien- texts. Each of the three fields of interest, nostalgia, utopia, and the pastoral tradition, are introduced in separate chapters. Special attention is given to the interrelations of the three fields. Their history, meaning, and functions are shortly elaborated and definitions applicable to their occurrences in fantasy texts are reached. In doing so, new categories and terms are proposed that enable a detailed analysis of the nostalgic, pastoral, and utopian properties of Tolkien- works. As nostalgia and utopia are important ingredients of pastoral writing, they are each introduced first and are finally related to a definition of the pastoral. The main part of this thesis applies the definitions and insights reached in the theoretical chapters to Tolkien- The Lord of the Rings and The Hobbit. This part is divided into three main sections. Again, the order of the chapters follows the line of argumentation. The first section contains the analysis of pastoral depictions in the two texts. Given the separation of the pastoral into different categories, which were outlined in the theoretical part, the chapters examine bucolic and georgic pastoral creatures and landscapes before turning to non-pastoral depictions, which are sub-divided into the antipastoral and the unpastoral. A separate chapter looks at the bucolic and georgic pastoral- positions and functions in the primary texts. This analysis is followed by a chapter on men- special position in Tolkien- mythology, as their depiction reveals their potential to be both pastoral and antipastoral. The second section of the analytical part is concerned with the role of nostalgia within pastoral culture. The focus is laid on the meaning and function of the different kinds of nostalgia, which were defined in the theoretical part, detectable in bucolic and georgic pastoral cultures. Finally, the analysis turns to the utopian potential of Tolkien- mythology. Again, the focus lies on the pastoral and non-pastoral creatures. Their utopian and dystopian visions are presented and contrasted. This way, different kinds of utopian vision are detected and set in relation to the overall dystopian fate of Tolkien- fictional universe. Drawing on the results of this thesis and on Terry Gifford- ecocritical work, the final chapter argues that Tolkien- texts can be defined as modern pastorals. The connection between Tolkien- work and pastoral literature made explicit in the analysis is thus cemented in generic terms. The conclusion presents a summary of the central findings of this thesis and introduces questions for further study.