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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.
This work is concerned with the numerical solution of optimization problems that arise in the context of ground water modeling. Both ground water hydraulic and quality management problems are considered. The considered problems are discretized problems of optimal control that are governed by discretized partial differential equations. Aspects of special interest in this work are inaccurate function evaluations and the ensuing numerical treatment within an optimization algorithm. Methods for noisy functions are appropriate for the considered practical application. Also, block preconditioners are constructed and analyzed that exploit the structure of the underlying linear system. Specifically, KKT systems are considered, and the preconditioners are tested for use within Krylov subspace methods. The project was financed by the foundation Stiftung Rheinland-Pfalz für Innovation and carried out in joint work with TGU GmbH, a company of consulting engineers for ground water and water resources.
Even though in most cases time is a good metric to measure costs of algorithms, there are cases where theoretical worst-case time and experimental running time do not match. Since modern CPUs feature an innate memory hierarchy, the location of data is another factor to consider. When most operations of an algorithm are executed on data which is already in the CPU cache, the running time is significantly faster than algorithms where most operations have to load the data from the memory. The topic of this thesis is a new metric to measure costs of algorithms called memory distance—which can be seen as an abstraction of the just mentioned aspect. We will show that there are simple algorithms which show a discrepancy between measured running time and theoretical time but not between measured time and memory distance. Moreover we will show that in some cases it is sufficient to optimize the input of an algorithm with regard to memory distance (while treating the algorithm as a black box) to improve running times. Further we show the relation between worst-case time, memory distance and space and sketch how to define "the usual" memory distance complexity classes.
Exposure to fine and ultra-fine environmental particles is still a problem of concern in many industrialized parts of the world and the intensified use of nanotechnology may further increase exposure to small particles. Since many years air pollution is recognized as a critical problem in western countries, which led to rigorous regulation of air quality and the introduction of strict guidelines. However, the upper thresholds for particulates in ambient air recommended by the world health organization are often exceeded several times in newly industrialized countries. Such high levels of air pollution have the potential to induce adverse effects on human health. The response triggered by air pollutants is not limited to local effects of the respiratory system but is often systemic, resulting in endothelial dysfunction or atherosclerotic malady. The link between air pollution and cardiovascular disease is now accepted by the scientific community but the underlying mechanisms responsible for the pro-atherogenic potential still need to be unraveled in detail. Based on the results from in- vivo and in vitro studies the production of reactive oxygen species due to exposure to particles is the most important mechanism to explain the observed adverse effects. However, the doses that were applied in many in vivo and in vitro studies are far beyond the range of what humans are exposed to and there is the need for more realistic exposure studies. Complex in vitro coculture systems may be valuable tools to study particle-induced processes and to extrapolate effects of particles on the lung. One of the objectives of this PhD thesis was the establishment and further improvement of a complex coculture system initially described by Alfaro-Moreno et al. [1]. The system is composed of an alveolar type-II cell line (A549), differentiated macrophage-like cells (THP-1), mast cells (HMC-1) and endothelial cells (EA.hy 926), seeded in a 3D-orientation on a microporous membrane to mimic the cell response of the alveolar surface in vitro in conjunction with native aerosol exposure (VitrocellTM chamber). The tetraculture system was carefully characterized to ensure its performance and repeatability of results. The spatial distribution of the cells in the tetraculture was analyzed by confocal laser scanning microscopy (CLSM), showing a confluent layer of endothelial and epithelial cells on both sides of the Transwellâ„¢. Macrophage-like cells and mast cells can be found on top of the epithelial cells. The latter cells formed colonies under submerged conditions, which disappeared at the air-liquid-interface (ALI). The VitrocellTM aerosol exposure system was not significantly influencing the viability. Using this system, cells were exposed to an aerosol of 50 nm SiO2-Rhodamine nanoparticles (NPs) in PBS. The distribution of the NPs in the tetraculture after exposure was evaluated by CLSM. Fluorescence from internalized particles was detected in CD11b-positive THP-1 cells only. Furthermore, all cell lines were found to be able to respond to xenobiotic model compounds, such as benzo[a]pyrene (B[a]P) or 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) with the upregulation of CYP1 mRNA. With this tetraculture system the response of the endothelial part of the alveolar barrier was studied in- vitro in a still realistic exposure scenario representing the conditions for a polluted situation without direct exposure of endothelial cells. After exposure to diesel exhaust particulate matter (DEPM) the expression of different anti-oxidant target genes and inflammatory genes such as NAD(P)H dehydrogenase quinone 1 (NQO1), superoxide dismutase 1 (SOD1) and heme oxygenase 1 (HMOX1), as well as the nuclear translocation nuclear factor erythroid-derived 2 (Nrf2) was evaluated. In addition, the potential of DEPM to induce the upregulation of CYP1A1 mRNA in the endothelium was analyzed. DEPM exposure led not to an upregulation of the anti-oxidant or inflammatory target genes, but to clear nuclear translocation of Nrf2. The endothelial cells responded to the DEPM treatment also with the upregulation of CYP1A1 mRNA and nuclear translocation of the aryl hydrocarbon receptor (AhR). Overall, DEPM triggered a response in the endothelial cells after indirect exposure of the tetraculture system to low doses of DEPM, underlining the sensitivity of ALI exposure systems. The use of the tetraculture together with the native aerosol exposure equipment may finally lead to a more realistic judgment regarding the hazard of new compounds and/or new nano-scaled materials in the future. For the first time, it was possible to study the response of the endothelial cells of the alveolar barrier in vitro in a realistic exposure scenario avoiding direct exposure of endothelial cells to high amounts of particulates.
Survey data can be viewed as incomplete or partially missing from a variety of perspectives and there are different ways of dealing with this kind of data in the prediction and the estimation of economic quantities. In this thesis, we present two selected research contexts in which the prediction or estimation of economic quantities is examined under incomplete survey data.
These contexts are first the investigation of composite estimators in the German Microcensus (Chapters 3 and 4) and second extensions of multivariate Fay-Herriot (MFH) models (Chapters 5 and 6), which are applied to small area problems.
Composite estimators are estimation methods that take into account the sample overlap in rotating panel surveys such as the German Microcensus in order to stabilise the estimation of the statistics of interest (e.g. employment statistics). Due to the partial sample overlaps, information from previous samples is only available for some of the respondents, so the data are partially missing.
MFH models are model-based estimation methods that work with aggregated survey data in order to obtain more precise estimation results for small area problems compared to classical estimation methods. In these models, several variables of interest are modelled simultaneously. The survey estimates of these variables, which are used as input in the MFH models, are often partially missing. If the domains of interest are not explicitly accounted for in a sampling design, the sizes of the samples allocated to them can, by chance, be small. As a result, it can happen that either no estimates can be calculated at all or that the estimated values are not published by statistical offices because their variances are too large.
Industrial companies mainly aim for increasing their profit. That is why they intend to reduce production costs without sacrificing the quality. Furthermore, in the context of the 2020 energy targets, energy efficiency plays a crucial role. Mathematical modeling, simulation and optimization tools can contribute to the achievement of these industrial and environmental goals. For the process of white wine fermentation, there exists a huge potential for saving energy. In this thesis mathematical modeling, simulation and optimization tools are customized to the needs of this biochemical process and applied to it. Two different models are derived that represent the process as it can be observed in real experiments. One model takes the growth, division and death behavior of the single yeast cell into account. This is modeled by a partial integro-differential equation and additional multiple ordinary integro-differential equations showing the development of the other substrates involved. The other model, described by ordinary differential equations, represents the growth and death behavior of the yeast concentration and development of the other substrates involved. The more detailed model is investigated analytically and numerically. Thereby existence and uniqueness of solutions are studied and the process is simulated. These investigations initiate a discussion regarding the value of the additional benefit of this model compared to the simpler one. For optimization, the process is described by the less detailed model. The process is identified by a parameter and state estimation problem. The energy and quality targets are formulated in the objective function of an optimal control or model predictive control problem controlling the fermentation temperature. This means that cooling during the process of wine fermentation is controlled. Parameter and state estimation with nonlinear economic model predictive control is applied in two experiments. For the first experiment, the optimization problems are solved by multiple shooting with a backward differentiation formula method for the discretization of the problem and a sequential quadratic programming method with a line search strategy and a Broyden-Fletcher-Goldfarb-Shanno update for the solution of the constrained nonlinear optimization problems. Different rounding strategies are applied to the resulting post-fermentation control profile. Furthermore, a quality assurance test is performed. The outcomes of this experiment are remarkable energy savings and tasty wine. For the next experiment, some modifications are made, and the optimization problems are solved by using direct transcription via orthogonal collocation on finite elements for the discretization and an interior-point filter line-search method for the solution of the constrained nonlinear optimization problems. The second experiment verifies the results of the first experiment. This means that by the use of this novel control strategy energy conservation is ensured and production costs are reduced. From now on tasty white wine can be produced at a lower price and with a clearer conscience at the same time.
Monetary Policy During Times of Crisis - Frictions and Non-Linearities in the Transmission Mechanism
(2017)
For a long time it was believed that monetary policy would be able to maintain price stability and foster economic growth during all phases of the business cycle. The era of the Great Moderation, often also called the Volcker-Greenspan period, beginning in the mid 1980s was characterized by a decline in volatility of output growth and inflation among the industrialized countries. The term itself is first used by Stock and Watson (2003). Economist have long studied what triggered the decline in volatility and pointed out several main factors. An important research strand points out structural changes in the economy, such as a decline of volatility in the goods producing sector through better inventory controls and developments in the financial sector and government spending (McConnell2000, Blanchard2001, Stock2003, Kim2004, Davis2008). While many believed that monetary policy was only 'lucky' in terms of their reaction towards inflation and exogenous shocks (Stock2003, Primiceri2005, Sims2006, Gambetti2008), others reveal a more complex picture of the story. Rule based monetary policy (Taylor1993) that incorporates inflation targeting (Svensson1999) has been identified as a major source of inflation stabilization by increasing transparency (Clarida2000, Davis2008, Benati2009, Coibion2011). Apart from that, the mechanics of monetary policy transmission have changed. Giannone et al. (2008) compare the pre-Great Moderation era with the Great Modertation and find that the economies reaction towards monetary shocks has decreased. This finding is supported by Boivin et al. (2011). Similar to this, Herrera and Pesavento (2009) show that monetary policy during the Volcker-Greenspan period was very effective in dampening the effects of exogenous oil price shocks on the economy, while this cannot be found for the period thereafter. Yet, the subprime crisis unexpectedly hit worldwide economies and ended the era of Great Moderation. Financial deregulation and innovation has given banks opportunities for excessive risk taking, weakened financial stability (Crotty2009, Calomiris2009) and led to the build-up of credit-driven asset price bubbles (SchularickTaylor2012). The Federal Reserve (FED), that was thought to be the omnipotent conductor of price stability and economic growth during the Great Moderation, failed at preventing a harsh crisis. Even more, it did intensify the bubble with low interest rates following the Dotcom crisis of the early 2000s and misjudged the impact of its interventions (Taylor2009, Obstfeld2009). New results give a more detailed explanation on the question of latitude for monetary policy raised by Bernanke and suggest the existence of non-linearities in the transmission of monetary policy. Weise (1999), Garcia and Schaller (2002), Lo and Piger (2005), Mishkin (2009), Neuenkirch (2013) and Jannsen et al. (2015) find that monetary policy is more potent during times of financial distress and recessions. Its effectiveness during 'normal times' is much weaker or even insignificant. This prompts the question if these non-linearities limit central banks ability to lean against bubbles and financial imbalances (White2009, Walsh2009, Boivin2010, Mishkin2011).
The argan woodlands of South Morocco represent an open-canopy dryland forest with traditional silvopastoral usage that includes browsing by goats, sheep and camels, oil production as well as agricultural use. In the past, these forests have undergone extensive clearing, but are now protected by the state. However, the remaining argan woodlands are still under pressure from intensive grazing and illegal firewood collection. Although the argan-forest area seems to be overall decreasing due to large forest clearings for intensive agriculture, little quantitative data is available on the dynamics and overall state of the remaining argan forest. To determine how the argan woodlands in the High Atlas and the Anti-Atlas had changed in tree-crown cover from 1972 to 2018 we used historical black and white HEXAGON satellite images as well as recent WorldView satellite images (see Part A of our study). Because tree shadows can oftentimes not be separated from the tree crown on panchromatic satellite images, individual trees were mapped in three size categories to determine if trees were unchanged, had decreased/increased in crown size or had disappeared or newly grown. The current state of the argan trees was evaluated by mapping tree architectures in the field. Tree-cover changes varied highly between the test sites. Trees that remained unchanged between 1972 and 2018 were in the majority, while tree mortality and tree establishment were nearly even. Small unchanged trees made up 48.4% of all remaining trees, of these 51% showed degraded tree architectures. 40% of small (re-) grown trees were so overbrowsed that they only appeared as bushes, while medium (3–7 m crown diameter) and large trees (>7 m) showed less degraded trees regardless if they had changed or not. Approaches like grazing exclusion or cereal cultivation lead to a positive influence on tree architecture and less tree-cover decrease. Although the woodland was found to be mostly unchanged 1972–2018, the analysis of tree architecture reveals that a lot of (mostly small) trees remained stable but in a degraded state. This stability might be the result of the small trees’ high degradation status and shows the heavy pressure on the argan forest.
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 × 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.
The midcingulate cortex has become the focus of scientific interest as it has been associated with a wide range of attentional phenomena. This survey found evidence indicating the relevance of gender and handedness for measures of regional cortical morphology. Although gender was associated with structural variations concerning the neuroanatomy of the midcingulum bundle as well, handedness did not emerge in the analyses of white matter characteristics as significant factor. Hemispheric differences were found at the level of both gray and white matter. Turning to the functional implications of neuroanatomical variations and comparing subjects with a pronounced and a low degree of midcingulate folding, which indicates differential expansions of cytoarchitectural areas, behavioral and electrophysiological differences in the processing of interference became evident. A high degree of leftward midcingulate fissurization was associated with better behavioral performance, presumably caused by a more effective conflict-monitoring system triggering fast and automatic attentional filtering mechanisms. Subjects exhibiting a lower degree of midcingulate fissurization rather seem to rely on more effortful control processes. These results carry implications not only concerning neuronal representations of individual differences in attentional processes, but might also be of relevance for the refinement of models for mental disorders.