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This working paper outlines analytical pathways that could contribute to deepening the understanding of water inequalities in cities of the Global South. It brings together the status quo of research on water inequalities in Accra, the capital of Ghana, and studies on Environmental Justice. In doing so, it argues for the need to analytically distinguish between the terms ‘(in)equality’ and ‘(in)justice’. Studying everyday water practices and per- spectives on water (in)justice of different stakeholders would be a suitable entry point for an in-depth ethnographic study that analytically separates water inequalities and water injustices but considers their interlinkages. The working paper is based on a literature review conducted in 2015 in the scope of the WaterPower project.

Both water scarcity and flood risk are increasingly turning into safety concerns for many urban dwellers and, consequently, become increasingly politicised. This development involves a reconfiguration of the academic land- scape around urban risk, vulnerability and adaptation to climate change research. This paper is a literature assessment of concepts on disaster risk, vulnerability and adaptation and their applicability to the context of studying water in an African city. An overview on water-related risk in African cities is presented and concepts and respective disciplinary backgrounds reviewed. Recent debates that have emerged from the application of risk, vulnerability and adaptation concepts in research and policy practice are presented. Finally the applicability of these concepts as well as the relevance and implications of recent debates for studying water in African cities is discussed. ‘Riskscape’ is proposed as a conceptual frame for close and integrated analysis of water related risk in an African city.

This thesis is divided into three main parts: The description of the calibration problem, the numerical solution of this problem and the connection to optimal stochastic control problems. Fitting model prices to given market prices leads to an abstract least squares formulation as calibration problem. The corresponding option price can be computed by solving a stochastic differential equation via the Monte-Carlo method which seems to be preferred by most practitioners. Due to the fact that the Monte-Carlo method is expensive in terms of computational effort and requires memory, more sophisticated stochastic predictor-corrector schemes are established in this thesis. The numerical advantage of these predictor-corrector schemes ispresented and discussed. The adjoint method is applied to the calibration. The theoretical advantage of the adjoint method is discussed in detail. It is shown that the computational effort of gradient calculation via the adjoint method is independent of the number of calibration parameters. Numerical results confirm the theoretical results and summarize the computational advantage of the adjoint method. Furthermore, provides the connection to optimal stochastic control problems is proven in this thesis.

Matching problems with additional resource constraints are generalizations of the classical matching problem. The focus of this work is on matching problems with two types of additional resource constraints: The couple constrained matching problem and the level constrained matching problem. The first one is a matching problem which has imposed a set of additional equality constraints. Each constraint demands that for a given pair of edges either both edges are in the matching or none of them is in the matching. The second one is a matching problem which has imposed a single equality constraint. This constraint demands that an exact number of edges in the matching are so-called on-level edges. In a bipartite graph with fixed indices of the nodes, these are the edges with end-nodes that have the same index. As a central result concerning the couple constrained matching problem we prove that this problem is NP-hard, even on bipartite cycle graphs. Concerning the complexity of the level constrained perfect matching problem we show that it is polynomially equivalent to three other combinatorial optimization problems from the literature. For different combinations of fixed and variable parameters of one of these problems, the restricted perfect matching problem, we investigate their effect on the complexity of the problem. Further, the complexity of the assignment problem with an additional equality constraint is investigated. In a central part of this work we bring couple constraints into connection with a level constraint. We introduce the couple and level constrained matching problem with on-level couples, which is a matching problem with a special case of couple constraints together with a level constraint imposed on it. We prove that the decision version of this problem is NP-complete. This shows that the level constraint can be sufficient for making a polynomially solvable problem NP-hard when being imposed on that problem. This work also deals with the polyhedral structure of resource constrained matching problems. For the polytope corresponding to the relaxation of the level constrained perfect matching problem we develop a characterization of its non-integral vertices. We prove that for any given non-integral vertex of the polytope a corresponding inequality which separates this vertex from the convex hull of integral points can be found in polynomial time. Regarding the calculation of solutions of resource constrained matching problems, two new algorithms are presented. We develop a polynomial approximation algorithm for the level constrained matching problem on level graphs, which returns solutions whose size is at most one less than the size of an optimal solution. We then describe the Objective Branching Algorithm, a new algorithm for exactly solving the perfect matching problem with an additional equality constraint. The algorithm makes use of the fact that the weighted perfect matching problem without an additional side constraint is polynomially solvable. In the Appendix, experimental results of an implementation of the Objective Branching Algorithm are listed.

Floods are hydrological extremes that have enormous environmental, social and economic consequences.The objective of this thesis was a contribution to the implementation of a processing chain that integrates remote sensing information into hydraulic models. Specifically, the aim was to improve water elevation and discharge simulations by assimilating microwave remote sensing-derived flood information into hydraulic models. The first component of the proposed processing chain is represented by a fully automated flood mapping algorithm that enables the automated, objective, and reliable flood extent extraction from Synthetic Aperture Radar images, providing accurate results in both rural and urban regions. The method operates with minimum data requirements and is efficient in terms of computational time. The map obtained with the developed algorithm is still subject to uncertainties, both introduced by the flood mapping algorithm and inherent in the image itself. In this work, particular attention was given to image uncertainty deriving from speckle. By bootstrapping the original satellite image pixels, several synthetic images were generated and provided as input to the developed flood mapping algorithm. From the analysis performed on the mapping products, speckle uncertainty can be considered as a negligible component of the total uncertainty. In the final step of the proposed processing chain real event water elevations, obtained from satellite observations, were assimilated in a hydraulic model with an adapted version of the Particle Filter, modified to work with non-Gaussian distribution of observations. To deal with model structure error and possibly biased observations, a global and a local weight variant of the Particle Filter were tested. The variant to be preferred depends on the level of confidence that is attributed to the observations or to the model. This study also highlighted the complementarity of remote sensing derived and in-situ data sets. An accurate binary flood map represents an invaluable product for different end users. However, deriving from this binary map additional hydraulic information, such as water elevations, is a way of enhancing the value of the product itself. The derived data can be assimilated into hydraulic models that will fill the gaps where, for technical reasons, Earth Observation data cannot provide information, also enabling a more accurate and reliable prediction of flooded areas.

In the first part of this work we generalize a method of building optimal confidence bounds provided in Buehler (1957) by specializing an exhaustive class of confidence regions inspired by Sterne (1954). The resulting confidence regions, also called Buehlerizations, are valid in general models and depend on a designated statistic'' that can be chosen according to some desired monotonicity behaviour of the confidence region. For a fixed designated statistic, the thus obtained family of confidence regions indexed by their confidence level is nested. Buehlerizations have furthermore the optimality property of being the smallest (w.r.t. set inclusion) confidence regions that are increasing in their designated statistic. The theory is eventually applied to normal, binomial, and exponential samples. The second part deals with the statistical comparison of pairs of diagnostic tests and establishes relations 1. between the sets of lower confidence bounds, 2. between the sets of pairs of comparable lower confidence bounds, and 3. between the sets of admissible lower confidence bounds in various models for diverse parameters of interest.

In recent years, the study of dynamical systems has developed into a central research area in mathematics. Actually, in combination with keywords such as "chaos" or "butterfly effect", parts of this theory have been incorporated in other scientific fields, e.g. in physics, biology, meteorology and economics. In general, a discrete dynamical system is given by a set X and a self-map f of X. The set X can be interpreted as the state space of the system and the function f describes the temporal development of the system. If the system is in state x âˆˆ X at time zero, its state at time n âˆˆ N is denoted by f^n(x), where f^n stands for the n-th iterate of the map f. Typically, one is interested in the long-time behaviour of the dynamical system, i.e. in the behaviour of the sequence (f^n(x)) for an arbitrary initial state x âˆˆ X as the time n increases. On the one hand, it is possible that there exist certain states x âˆˆ X such that the system behaves stably, which means that f^n(x) approaches a state of equilibrium for nâ†’âˆž. On the other hand, it might be the case that the system runs unstably for some initial states x âˆˆ X so that the sequence (f^n(x)) somehow shows chaotic behaviour. In case of a non-linear entire function f, the complex plane always decomposes into two disjoint parts, the Fatou set F_f of f and the Julia set J_f of f. These two sets are defined in such a way that the sequence of iterates (f^n) behaves quite "wildly" or "chaotically" on J_f whereas, on the other hand, the behaviour of (f^n) on F_f is rather "nice" and well-understood. However, this nice behaviour of the iterates on the Fatou set can "change dramatically" if we compose the iterates from the left with just one other suitable holomorphic function, i.e. if we consider sequences of the form (gâˆ˜f^n) on D, where D is an open subset of F_f with f(D)âŠ‚ D and g is holomorphic on D. The general aim of this work is to study the long-time behaviour of such modified sequences. In particular, we will prove the existence of holomorphic functions g on D having the property that the behaviour of the sequence of compositions (gâˆ˜f^n) on the set D becomes quite similarly chaotic as the behaviour of the sequence (f^n) on the Julia set of f. With this approach, we immerse ourselves into the theory of universal families and hypercyclic operators, which itself has developed into an own branch of research. In general, for topological spaces X, Y and a family {T_i: i âˆˆ I} of continuous functions T_i:Xâ†’Y, an element x âˆˆ X is called universal for the family {T_i: i âˆˆ I} if the set {T_i(x): i âˆˆ I} is dense in Y. In case that X is a topological vector space and T is a continuous linear operator on X, a vector x âˆˆ X is called hypercyclic for T if it is universal for the family {T^n: n âˆˆ N}. Thus, roughly speaking, universality and hypercyclicity can be described via the following two aspects: There exists a single object which allows us, via simple analytical operations, to approximate every element of a whole class of objects. In the above situation, i.e. for a non-linear entire function f and an open subset D of F_f with f(D)âŠ‚ D, we endow the space H(D) of holomorphic functions on D with the topology of locally uniform convergence and we consider the map C_f:H(D)â†’H(D), C_f(g):=gâˆ˜f|_D, which is called the composition operator with symbol f. The transform C_f is a continuous linear operator on the Fréchet space H(D). In order to show that the above-mentioned "nice" behaviour of the sequence of iterates (f^n) on the set D âŠ‚ F_f can "change dramatically" if we compose the iterates from the left with another suitable holomorphic function, our aim consists in finding functions g âˆˆ H(D) which are hypercyclic for C_f. Indeed, for each hypercyclic function g for C_f, the set of compositions {gâˆ˜f^n|_D: n âˆˆ N} is dense in H(D) so that the sequence of compositions (gâˆ˜f^n|_D) is kind of "maximally divergent" " meaning that each function in H(D) can be approximated locally uniformly on D via subsequences of (gâˆ˜f^n|_D). This kind of behaviour stands in sharp contrast to the fact that the sequence of iterates (f^n) itself converges, behaves like a rotation or shows some "wandering behaviour" on each component of F_f. To put it in a nutshell, this work combines the theory of non-linear complex dynamics in the complex plane with the theory of dynamics of continuous linear operators on spaces of holomorphic functions. As far as the author knows, this approach has not been investigated before.

Evapotranspiration (ET) is one of the most important variables in hydrological studies. In the ET process, energy exchange and water transfer are involved. ET consists of transpiration and evaporation. The amount of plants transpiration dominates in ET. Especially in the forest regions, the ratio of transpiration to ET is in general 80-90 %. Meteorological variables, vegetation properties, precipitation and soil moisture are critical influence factors for ET generation. The study area is located in the forest area of Nahe catchment (Rhineland-Palatinate, Germany). The Nahe catchment is highly wooded. About 54.6 % of this area is covered by forest, with deciduous forest and coniferous forest are two primary types. A hydrological model, WaSiM-ETH, was employed for a long-term simulation from 1971-2003 in the Nahe catchment. In WaSiM-ETH, the potential evapotranspiration (ETP) was firstly calculated by the Penman-Monteith equation, and subsequently reduced according to the soil water content to obtain the actual evapotranspiration (ETA). The Penman-Monteith equation has been widely used and recommended for ETP estimation. The difficulties in applying this equation are the high demand of ground-measured meteorological data and the determination of surface resistance. A method combined remote sensing images with ground-measured meteorological data was also used to retrieve the ETA. This method is based on the surface properties such as surface albedo, fractional vegetation cover (FVC) and land surface temperature (LST) to obtain the latent heat flux (LE, corresponding to ETA) through the surface energy balance equation. LST is a critical variable for surface energy components estimation. It was retrieved from the TM/ETM+ thermal infrared (TIR) band. Due to the high-quality and cloudy-free requirements for TM/ETM+ data selection as well as the overlapping cycle of TM/ETM+ sensor is 16 days, images on only five dates are available during 1971-2003 (model ran) " May 15, 2000, July 05, 2001, July 19, August 04 and September 21 in 2003. It is found that the climate conditions of 2000, 2001 and 2003 are wet, medium wet and dry, respectively. Therefore, the remote sensing-retrieved observations are noncontinuous in a limited number over time but contain multiple climate conditions. Aerodynamic resistance and surface resistance are two most important parameters in the Penman-Monteith equation. However, for forest area, the aerodynamic resistance is calculated by a function of wind speed in the model. Since transpiration and evaporation are separately calculated by the Penman-Monteith equation in the model, the surface resistance was divided into canopy surface resistance rsc and soil surface resistance rse. rsc is related to the plants transpiration and rse is related to the bare soil evaporation. The interception evaporation was not taken into account due to its negligible contribution to ET rate under a dry-canopy (no rainfall) condition. Based on the remote sensing-retrieved observations, rsc and rse were calibrated in the WaSiM-ETH model for both forest types: for deciduous forest, rsc = 150 smâˆ’1, rse = 250 smâˆ’1; for coniferous forest, rsc = 300 smâˆ’1, rse = 650 smâˆ’1. We also carried out sensitivity analysis on rsc and rse. The appropriate value ranges of rsc and rse were determined as (annual maximum): for deciduous forest, [100,225] smâˆ’1 for rsc and [50,450] smâˆ’1 for rse; for coniferous forest, [225,375] smâˆ’1 for rsc and [350,1200] smâˆ’1 for rse. Due to the features of the observations that are in a limited number but contain multiple climate conditions, the statistical indices for model performance evaluation are required to be sensitive to extreme values. In this study, boxplots were found to well exhibit the model performance at both spatial and temporal scale. Nush-Sutcliffe efficiency (NSE), RMSE-observations standard deviation ratio (RSR), percent bias (PBIAS), mean bias error (MBE), mean variance of error distribution (S2d), index of agreement (d), root mean square error (RMSE) were found as appropriate statistical indices to provide additional evaluation information to the boxplots. The model performance can be judged as satisfactory if NSE > 0.5, RSR â‰¤ 0.7, PBIAS < -±12, MBE < -±0.45, S2d < 1.11, d > 0.79, RMSE < 0.97. rsc played a more important role than rse in ETP and ETA estimation by the Penman-Monteith equation, which is attributed to the fact that transpiration dominates in ET. The ETP estimation was found the most correlated to the relative humidity (RH), followed by air temperature (T), relative sunshine duration (SSD) and wind speed (WS). Under wet or medium wet climate conditions, ETA estimation was found the most correlated to T, followed by RH, SSD and WS. Under a water-stress condition, there were very small correlations between ETA and each meteorological variable.

The last decades of stress research have yielded substantial advancements highlighting the importance of the phenomenon for basic psychological functions as well as physical health and well-being. Progress in stress research heavily relies on the availability of suitable and well validated laboratory stressors. Appropriate laboratory stressors need to be able to reliably provoke a response in the relevant parameters and be applicable in different research settings or experimental designs. This thesis focuses on the Cold Pressor Test (CPT) as a stress induction technique. Three published experiments are presented that show how the advantages of the CPT can be used to test stress effects on memory processes and how some of its disadvantages can be met by a simple modification that retains its feasibility and validity. The first experiment applies the CPT in a substantial sample to investigate the consolidation effects of post-learning sympathetic arousal. Stressed participants with high increases in heart rate during the CPT showed enhanced memory performance one day after learning compared to both the warm water control group and low heart rate responders. This finding suggests that beta-adrenergic activation elicited shortly after learning enhances memory consolidation and that the CPT induced heart rate response is a predictor for this effect. Moreover, the CPT proved to be an appropriate stressor to test hypothesis about endogenous adrenergic effects on memory processes. The second experiment addresses known practical limitations of the standard dominant hand CPT protocol. A bilateral feet CPT modification is presented, the elicited neuroendocrine stress response assessed and validated against the standard CPT in a within-subjects design. The bilateral feet CPT elicited a substantial neuroendocrine stress response. Moreover, with the exception of blood pressure responses, all stress parameters were enhanced compared to the standard CPT. This shows that the bilateral feet CPT is a valid alternative to the standard CPT. The third experiment further validates the bilateral feet CPT and its corresponding control procedure by employing it in a typical application scenario. Specifically, the bilateral feet CPT was used to modulate retrieval of event files in a distractor-response binding paradigm that required lateralized bimanual responses. Again, the bilateral feet CPT induced significant increases in heart rate, blood pressure and cortisol, no such increases could be observed in the warm water control condition. Moreover, stressed participants showed diminished retrieval compared to controls. These results provide further evidence for the feasibility and validity of the bilateral feet CPT and its warm water control procedure. Together the experiments presented here highlight the usefulness of the CPT as a tool in psychophysiological stress research. It is especially well suited to test hypothesis concerning stress effects on memory processes and its applicability can be further increased by the bilateral feet modification.

Climate change and habitat fragmentation modify the natural habitat of many wetland biota and lead to new compositions of biodiversity in these ecosystems. While the direct effects of climate are often well known, indirect effects due to biotic interactions remain poorly understood. The water meadow grasshopper, Chorthippus montanus, is a univoltine habitat specialist, which is adapted to permanently moist habitats. Land use change and drainage led to highly fragmented populations of this generally flightless species. In large parts of the Palaearctic Ch. montanus occurs sympatrically with its widespread congener, the meadow grasshopper Chorthippus parallelus. Due to their close relationship and their similar songs, hybridization is likely to occur in syntopic populations. Such a species pair of a habitat specialist and a habitat generalist represents an ideal model system to examine the role of ongoing climate change and an accumulation of extreme climatic events on the life history strategies, population dynamics and inter-specific interactions. In Chapter I a laboratory experiment was conducted to identify the impact of environmental factors on intra-specific life-history traits of Ch. montanus. Like other Orthoptera species, Ch. montanus follows a converse temperature size rule. In line with the dimorphic niche hypothesis, which states that sexual size dimorphism evolved in response to the different sexual reproductive roles, both sexes showed different responses to increasing density at lower temperatures. Males attained smaller body sizes at high densities, whereas females had a prolonged development time. This is the first evidence for a sex-specific phenotypic plasticity in Ch. montanus. Females benefit from the prolonged development as their reproductive success depends on the size and number of egg clutches they may produce. By contrast, the reproductive success of males depends on the chance to fertilize virgin females, which increases with faster development. This may become a disadvantage for Ch. montanus as an intraspecific phenology shift may increase hybridization risk with the sibling species. Despite the widespread assumption that hybridization between two sympatric species is rare due to complete reproductive barriers, the genetic analyses of 16 populations (Chapter II) provided evidence for wide prevalence of hybridization between both species in the wild. As no complete admixture was found in the examined population, it is assumed that hybridization only occurs in ecotones between wetlands and drier parts. Reproductive barriers (habitat isolation, behavior, phenology) seem to prevent the genetic swamping of Ch. montanus populations. Although a behavioral experiment showed that mate choice presents an important reproductive barrier between both species, the experiment also revealed that reproductive barriers could be altered by environmental change (e.g. increasing heterospecific frequency). Chapter III analyzes the impact of extreme climatic events on population dynamics and interspecific hybridization. A mark-recapture analysis combined with weather records over five years provides evidence that the embryonic development in Ch. montanus is vulnerable to extreme climatic events. Strong population declines in Ch. montanus lead to a disequilibrium between Ch. montanus and Ch. parallelus populations and increases the risk of hybridization. The highest hybridization risk was found in the first weeks of a season, when both species had an overlapping phenology. Furthermore, hybrids were generally localized at the edge of the Ch. montanus distribution with higher heterospecific encounter probabilities. The hybridization rate reached up to 19.6%. The genetic analyses in Chapter II and III show that hybridization differentially affects specialists and generalists. While generalists may benefit from hybridization by an increasing genetic diversity, such a positive correlation was not found for Ch. montanus. The results underline the importance of reproductive barriers for the co-existence of these sympatric species. However, climate change and other anthropogenic disturbances alter reproductive barriers and promote hybridization, which may threaten small populations by genetic displacement. As anthropogenic hybridization is recognized as a major threat to biodiversity, it should be considered in environmental law and policy. In Chapter IV the role of hybrids and hybridization in three levels of law and the historical backgrounds of hybrids becoming a part of legal instruments is analyzed. Due to legal uncertainties and the complexity of this topic a legal assessment of hybrids is challenging and argues for species-specific approaches. Nonetheless, existing legal norms provide a suitable basis, but need to be specified. Finally, this chapter discusses different opportunities for the management of hybrids and hybridization in a conservation perspective and their necessity.