459 search hits
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The Integrated Size and Price Optimization problem
(2012)
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Miriam Kießling
Sascha Kurz
Jörg Rambau
- We present the Integrated Size and Price Optimization Problem (ISPO)
for a fashion discounter with many branches. Based on a two-stage
stochastic programming model with recourse, we develop an exact
algorithm and a production-compliant heuristic that produces small
optimality gaps. In a field study we show that a distribution of
supply over branches and sizes based on ISPO solutions is
significantly better than a one-stage optimization of the
distribution ignoring the possibility of optimal pricing.
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Shape Calculus Applied to Elliptic Optimal Control Problems
(2012)
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Michael Frey
- This thesis is devoted to the analysis of a very simple, pointwisely state-constrained optimal control problem of an elliptic partial differential equation. The transfer of an idea from the field of optimal control of ordinary differential equations, which proved fruitful with respect to both theoretical treatment and design of algorithms, is the starting point. On this, the state inequality constraint, which is regarded as an equation inside the active set, is differentiated in order to obtain a control law.
A geometrical splitting of the constraints is necessary to carry over this approach to the chosen model problem. The associated assertions are rigorously ensured. The subsequent derivation of a control law in the sense of the abovementioned idea yields an equivalent reformulation of the model problem. The active set appears as an independent and equal optimization variable in this new formulation. Thereby a new class of optimization problem is established, which forms a hybrid of optimal control and shape-/topology optimization: set optimal control. This class is integrated into the very abstract framework of optimization on vector bundles; for that purpose some important notions from the field of calculus on manifolds are introduced and related with shape calculus.
First order necessary conditions of the set optimal control problem are derived by means of two different approaches: on the one hand a reduced approach via the elimination of the state variable, which uses a formulation as bilevel optimization problem, is pursued, and on the other hand a formal Lagrange principle is presented.
A comparison of the newly obtained optimality conditions with those known form literature yields relations between the Lagrange multipliers; in particular, it becomes apparent that the new approach involves higher regularity. The comparison is embedded to the theory of partial differential-algebraic equations, and it is shown that the new approach yields a reduction of the differential index.
Upon investigation of the gradient and the second covariant derivative of the objective functional different Newton- and trial algorithms are presented and discussed in detail. By means of a comparison with the well-established primal-dual active set method different benefits of the new approach become apparent. In particular, the new algorithms can be formulated in function space without any regularization. Some numerical tests illustrate that an efficient and competitive solution of state-constrained optimal control problems is achieved.
The whole work gives numerous references to different mathematical disciplines and encourages further investigations. All in all, it should be regarded as a first step towards a more comprehensive perspective on state-constrained optimal control of partial differential equations.
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Beyond productivity- Effects of extreme weather events on ecosystem processes and biotic interactions
(2012)
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Julia Walter
- Under global climate change, extreme weather events, such as heat waves, drought or heavy rain spells, are projected to increase in magnitude and frequency. As these may affect vegetation and ecosystems more than gradual shifts in mean climatic parameters, investigating the consequences of extreme weather events recently became an important issue in climate change research. The main focus of most experiments investigating effects of extreme weather events on vegetation is on primary productivity. In our experiment in artificially planted communities, even an extreme drought of 1000-year recurrence did not have effects on above- or below-ground biomass production from 2005-2010.
Thus, the main objectives of this thesis were (1) to investigate if extreme weather events have an effect on ecosystem functions beyond productivity, (2) to test if such a high resistance or resilience in response to drought regarding productivity also exists in more naturally grown plant communities and (3) to further elucidate possible mechanisms of the surprisingly large stability of the plant communities.
To investigate these objectives, several experimental studies were conducted in artificially planted, as well as in naturally grown grassland communities and consequences of extreme weather events for ecosystem processes, such as decomposition and herbivory were investigated. In a pot experiment, it was studied, if grass plants react improved towards repeated drought when compared to a first drought and thus reveal a kind of drought memory. Such a memory might be one possible, but up until now widely neglected mechanism of resilience.
Even though biomass production remained stable in our experiment in artificially planted communities, biomass quality was severely affected by extreme drought, thereby strongly affecting the development of a herbivore caterpillar feeding on drought-exposed leaves. Further, plant compounds of the host plant depended on the composition of the plant community it was grown in. This in turn resulted in strong effects on the larval mortality of herbivores feeding on such plants.
In contrast to the study in artificially planted communities, aboveground net primary productivity (ANPP) was reduced in naturally composed grassland in response to extreme rainfall variability, including an extreme drought followed by heavy rainfall. Forage quality was altered by drought. Furthermore, mowing frequency strongly altered forage quality and biomass production, but did not interact with rainfall variability and thus did neither buffer, nor amplify effects of extreme rainfall variability. Despite effects of rainfall variability on ANPP, grassland showed high resilience after drought followed by heavy rain, as effects were large shortly after the extreme event, but did not persist until a second harvest later in the year.
In natural grassland, rainfall variability and drought also affected ecosystem processes, here litter decomposition, beyond productivity. Drought followed by heavy rain pulses decreased decomposition rates. Decomposition in more frequently mown meadows was more vulnerable towards drought exposure. Winter warming and additional winter rain had no long-term effect on decomposition. To conclude, projected increases in drought frequency under climate change may inhibit decomposition and alter nutrient and carbon cycling along with soil quality in temperate grassland, whereas a reduction of snow cover leading to more variable soil surface temperatures may counteract increased decomposition under winter warming.
In this thesis, an ecological stress memory as one possible mechanism of resilience is defined as any response of a single plant after a stress experience that improves the reaction of the plant towards future stress experience and which is assessed on a whole plant level. This thesis further provides evidence of a drought memory in grass plants: Plants repeatedly subjected to drought showed improved photo-protection and a higher rate of living biomass when compared to plants faced with their first drought. Similarly, tree seedlings exposed to drought in summer revealed higher frost resistance during winter, providing evidence of a long-lasting “cross-stress-memory” .
To sum up, the thesis shows that extreme weather events, even though neither severely affecting biomass production in artificially composed, nor in naturally growing communities in the long-term, exert strong influence on physiological or biogeochemical parameters, such as plant compounds or soil biotic activity. These changes in turn modify ecosystem functions beyond productivity, for example herbivory or decomposition, possibly altering biotic interactions and nutrient cycling. Furthermore, the findings imply that plants exhibit a stress memory after stress exposure, which may be one mechanisms leading to a high stability and resilience upon frequent stress.
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The peptidyl-prolyl isomerase Pin1 is required for maintenance of the spindle assembly checkpoint
(2012)
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Andreas Brown
- Chromosomes are replicated during S-phase and segregated during M-phase of the eukaryotic cell cycle. The two sister chromatids of each duplicated chromosome are topologically entrapped and, thus, paired by the ring-shaped protein complex cohesin. They are separated in anaphase of mitosis when cohesin is endoproteolytically cleaved by separase. Activation of this giant protease requires the degradation of its two inhibitors, securin and cyclin B1, which is mediated by the anaphase promoting complex or cyclosome (APC/C), a multisubunit ubiquitin ligase, in conjunction with its essential co-activator Cdc20.
The spindle assembly checkpoint (SAC) is a surveillance mechanism that monitors the chromosomes' interactions with the microtubules of the mitotic spindle apparatus. In response to even one erroneous attachment the affected kinetochore emits a "wait anaphase" signal, which is amplified and culminates in the quantitative sequestration of Cdc20 by the SAC components Mad2 and BubR1. The consequent inactivation of the APC/C causes a metaphase arrest and gives the cell time to correct the error. Given its great importance for chromosome segregation fidelity, it comes at no surprise that loss of the SAC causes cell death while its curtailing is associated with tumour formation.
Pin1 is a peptidyl-prolyl-isomerase with strong preference for phosphorylated Ser-Pro or Thr-Pro motives within its protein substrates. In the present thesis, evidence for the involvement of Pin1 in the maintenance of a robust SAC response is presented.
Antibodies against Pin1 were raised and used to establish the effective immunodepletion of Pin1 from extracts of Xenopus laevis eggs. While the SAC could readily be activated in mock-treated samples of this cell free system, securin was degraded despite the presence of unattached kinetochores when Pin1 had previously been removed. Proving the specificity of this effect, a SAC mediated arrest could be rescued by adding back recombinant Pin1 to depleted extracts. Similarly, addition of dominant negative but not of wild-type Pin1 to SAC-arrested extracts resulted in a checkpoint override.
Chemical inhibition of human Pin1 with two different molecules in two different cancer cells lines invariably forced the cells to exit mitosis in the absence of spindles. This resulted in the premature disappearance of securin, cyclin B1 and a mitosis-specific phosphorylation on Ser10 of histone H3. Thus, Pin1's role as a checkpoint component is conserved in mammals.
In search for the relevant target, Cdc20 was identified as a novel interaction partner of vertebrate Pin1. This association requires phosphorylation of Cdc20 on Ser-Pro/Thr-Pro sites and occurs only during mitosis. Importantly, the Pin1-Cdc20 interaction is direct and not bridged via another checkpoint component or a subunit of the core APC/C. The experimental data suggest that Pin1-dependent isomerization of Cdc20 might bias it to preferentially associate with Mad2 and BubR1 instead of APC/C.
Taken together, these findings contribute to a better understanding of the molecular mechanisms involved in SAC signalling and unravel a previously unappreciated role of Pin1 for genome integrity.
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Trends, Discourses and Representations in Religions in Africa
(2012)
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Meron Zeleke
Halkano Abdi Wario
- Religion in Africa has for long been a woven cultural fabric of life, a great moving force that guided people’s behavior, interaction and action since time immemorial. A decade after the United States experience of the 9/11, the unfortunate event has set the landmark for a geopolitics in contemporary Africa that securitizes religious movements and that identify them with the so-called global war on terror, a phenomenon within which most African nations play a significant regional role. The current wave of developments related to religion in the contingent became fossilized through religious manipulation and politicization in the post-colonial era. Three thematic concepts have been identified, i.e., religious trends, cultural discourses and representation, in order to capture some of the most contemporary issues of concern to Muslim, Christian and indigenous religious communities in Africa. Nine papers in this second issue of BIGSAS Works! hence targeted current doctoral researches from a wide range of disciplines and successfully integrated a cross-disciplinary approach to appreciate the complexity of faith matters in the continent.
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The service-productivity learning cockpit – a business intelligence tool for service enterprises
(2012)
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Sebastian Walther
Gaurang Phadke
Torsten Eymann
- The paper describes the development of an agent-based simulation tool for hospital managers to manage their productivity of services, especially in the context of supporting services like patient transport logistics. The learning cockpit allows hospital managers to see how the change of inputs changes the overall perceived customer values of all stakeholders and therefore to get a visualization of the impacts their decisions cause. The paper introduces the general research domain service-productivity, followed by a description of the development steps of artefact creation. The learning cockpit is part of a research project called BELOUGA, which is funded by the German government.
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The Nature of Fluids in Hydrothermal Copper and Molybdenum Ore Deposits - An experimental and analytical study
(2012)
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Linda Lerchbaumer
- The evolution of magmatic-hydrothermal fluids in porphyry Cu and porphyry Mo deposits was studied using synthetic and natural fluid inclusions by optical microscopy, microthermometry, Raman spectroscopy, and LA-ICP-MS.
The partitioning of Cu between vapor and brine in aqueous NaCl-S ± KCl ± FeCl2-rich fluids was investigated by means of hydrothermal experiments in rapid quench autoclaves at 600-800°C, 70-130 MPa and at both oxidizing and reducing fO2, covering all geologically relevant conditions. Resulting partition coefficients (DCuvap/brine) are between 0.2 and 0.4 for the range of studied S-concentrations, fluid pH, fO2, and P-T conditions. These values indicate that Cu does not partition into the vapor phase at any plausible condition in contrast to data from natural quartz-hosted vapor and brine inclusions which appear to indicate Cu enrichment in the vapor.
The formation of such Cu-rich vapor-type fluid inclusions was investigated in hydrothermal re-equilibration experiments. For this purpose, coexisting vapor and brine inclusions of known composition were re-equilibrated in a fluid of slightly different composition and lower pH than the trapped one at 800°C, 70-130 MPa. This procedure led to a dramatic increase in Cu concentrations in the vapor phase from 0.3 ± 0.03 to 5.7 ± 3.3 wt% after re-equilibration and the change of DCuvap/brine from a true value of 0.4 ± 0.05 to an apparent value of 8.3 ± 4.9. This post-entrapment modification can be traced back to the difference in fluid pH between the trapped and the surrounding fluid, inducing diffusion of H+ out of the inclusion and the diffusion of Cu+ (and Na+, Ag+) into the inclusion in order to maintain charge balance. Moreover, the presence of larger amounts of S within vapor inclusions as compared to brine inclusions can bind larger amounts of Cu. The re-equilibration of trails of vapor and brine inclusions in a natural quartz sample in a fluid similar to the trapped one, yet more acidic, showed that this modification process can be reversed, resulting in the loss of major amounts of Cu from natural vapor inclusions.
The composition of metal-bearing melts and magmatic fluids of Mo-mineralized granites resembling porphyry Mo deposits was investigated using natural melt-, fluid-, and solid-inclusions in quartz crystals found in miarolitic cavities from minor Mo-occurrences in Colorado and Norway. Melt inclusions from the Treasure Mountain Dome are highly enriched in Mo (4-43 ppm), also melt inclusions from the Drammen and Glitrevann granites (5-32 ppm, and 12 ppm, respectively), resembling highly fractionated melts. Copper concentrations are low (<1-30 ppm) in the melts, but high in the fluids: intermediate density, supercritical fluid inclusions of these three locations host 6-1900 ppm, 8-3500 ppm, and 5-180 ppm Cu, respectively. The comparison of these results with data from economic porphyry Mo and porphyry Cu (Mo, Au) deposits shows no difference in Mo concentrations in the particular melts and fluids. Hence, other factors probably control the evolution of a granitic intrusion into large, economic Mo deposits, minor Mo occurrences, or just into barren plutons. These may be mainly the size, position, and geometry of the parental magma chamber, the multiplicity of intrusions maintaining a constant flux of metalliferous, S-rich, hot melts, and the extent of fluid focusing within small rock volumes forming high-grade ore shells.
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Irreducible symplectic complex spaces
(2012)
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Tim Kirschner
- In Chapter 1 we define period mappings of Hodge-de Rahm type for certain submersive, yet not necessarily locally topologically trivial, morphisms of complex manifolds. Generalizing Griffiths's theory, we interpret the differential of such period mappings as the composition of the Kodaira-Spencer map and a map derived from the sheaf cohomological cup product and the contraction of vector fields with differential forms.
In Chapter 2 of the text, we consider a submersive morphism $f\colon X\to S$ of complex spaces which is compactified by a proper, flat, and Kähler morphism $\bar f\colon \bar X\to S$. Taking into account the codimension of $\bar X\setminus X$ in $\bar X$, we draw conclusions about the degeneration behavior of the relative Frölicher spectral sequence of the morphism $f$ and about the local freeness of the modules $\mathrm{R}^qf_*(\Omega^p_f)$; our results can be viewed as relative generalizations of a theorem of Takeo Ohsawa.
In our final Chapter 3, we employ the upshots of the preceding two chapters in order to deduce a local Torelli theorem for irreducible symplectic complex spaces. As an application of the local Torelli theorem, we prove that irreducible symplectic complex spaces whose codimension of the singular locus does not deceed $4$ satisfy the so-called Fujiki relation.
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Experimental classification of divertor detachment
(2012)
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Steffen Potzel
- Avoiding damage of the divertor material by keeping the power load below a certain threshold is a major challenge for the operation of
future fusion devices such as ITER. For Tungsten, the foreseen ITER divertor target material, the
power load must be kept below 5 MW m^2 in continuous operation. This can in ITER only be achieved with the plasma
being detached or partially detached from the divertor.
Divertor detachment is characterized by a strong reduction of the ion flux to the target. With a reduction of the temperature,
achieved by increasing the main plasma density or by seeding additional impurities, volumetric processes such as charge exchange collisions
and recombination become dominant. These processes lead to a strong reduction of the ion flux and plasma pressure in front of the divertor target.
Although the single physical mechanisms leading to detachment seem to be understood, it was not yet possible to theoretically
simulate detachment correctly with respect to experimental observations. This means that some understanding of this process is still missing.
In the detached regime,
the region of high electron density is retracted from the target and a knowledge of the electron density distribution in the divertor
volume is necessary to understand the detachment process. In this context, a diagnostic determining the electron density in the
divertor volume, based on the spectroscopic measurement of the
Stark broadening of the Balmer lines, has been installed at ASDEX Upgrade. Initial problems with reflected stray-radiation have been
solved and first measurements were successfully compared for consistency with other diagnostics.
The detachment process was then investigated with an extensive set of density ramp discharges with different heating powers,
fuelling species and magnetic field directions. The density measurements in the divertor volume were combined with all other available
divertor diagnostics and a consistent picture of the detachment process was obtained. It was found that detachment is not a continuous
evolution
but undergoes three different states. During one of these states radiative fluctuations close to the X-point and high densities far away
from the separatrix occur. This is a situation which is not described by present day theoretical models.
Furthermore, it was shown that the conditions of both the inner and outer divertor are
strongly coupled and that the inner divertor even influences the outer divertor. This effect was not shown yet, neither experimentally
nor by theoretical simulations.
It was further discovered how additional puffing of nitrogen into the divertor, which removes power via radiation, changes the
detached divertor conditions and may even change the confined plasma conditions. The effect of an additional magnetic perturbation
field on the detachment process has also been investigated. Finally, an unstable situation was found, during which the divertor plasma
oscillates between two detachment states back and forth.
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Smart Hydrogels based on Responsive Star-Block Copolymers
(2012)
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Alexander Schmalz
- The work presented in this thesis is focused on the synthesis of double-responsive star-shaped block copolymers and their formation of smart hydrogels in response to different external stimuli, specifically temperature and pH. Our concept was based on (AB)x diblock copolymer stars where both blocks are responsive to temperature and pH. This approach led to physically crosslinked hydrogels, which could form/disintegrate in response to a first trigger, i.e. the outer B blocks are alternating between hydrophilic and hydrophobic. The mechanical properties of the gels could still be manipulated by a second, independent trigger, i.e. upon applying the second trigger, the inner A blocks contract, leading to a change in mechanical properties.
The first part deals with the synthesis and characterization of linear and star-shaped poly((2 diethylamino)ethyl methacrylate) (PDEA) to investigate its double-responsive behavior and its potential for the design of double-responsive gelators. This polymer responds to variations in both pH and temperature, just like the analogous poly((2 dimethylamino)ethyl methacrylate) (PDMA). At a given temperature PDEA exhibits a critical pH value above which the chains collapse and aggregation takes place. The temperature-responsive behavior of PDEA does not depend on molecular weight or architecture, i.e. arm number. However, the cloud point does strongly depend on pH, as it affects the overall charge of the star.
For the second part we combined PDMA and PDEA to create double-responsive star-shaped block copolymers (DMA-DEA)x where both blocks are responsive to pH and temperature. The collapse of the PDEA outer blocks is first selectively triggered by heating. This has been proven by dynamic light scattering and is due to the significantly lower cloud point of PDEA with respect to that of PDMA at identical pH. The gelation behavior was investigated in dependence on block length and arm number. At high concentrations hydrogel formation was observed under conditions where only the PDEA outer blocks are insoluble. Rheology measurements showed that a minimum DEA fraction is necessary for gel formation and that the DEA fraction strongly influences the properties of the gels. Another factor controlling the gelation behavior of the diblock copolymer stars is the pH value, as the sol-gel transition temperature at a given concentration is shifted to lower values upon increasing the pH. The mechanical properties of some gel can be manipulated, as a decrease in the storage modulus was only observed for soft gels, if the temperature is increased above the transition temperature of the inner PDMA block, i.e. when the PDMA blocks contract. Thus, we successfully created double-responsive star-shaped gelators which formed reversible hydrogels that were still able to respond to a second trigger. However, the aggregation and hydrogel formation turned to out to be quite complex, due to the high number of parameters controlling them.
Finally, our concept was extended to other polymers and simplified by changing the outer block of the block copolymer stars to a polymer that is only responsive to temperature. This allows for an easier tuning of the sol-gel transition, as only one parameter is involved. The new diblock stars are comprised of PDMA inner blocks and outer blocks of poly(diethylene glycol methyl ether methacrylate) (PDEGMA), which can be triggered independently of each other as confirmed by turbidimetry and dynamic light scattering. They form hydrogels at relatively low concentrations upon heating above the transition temperature of PDEGMA independent of the pH value. The fraction of DEGMA is an important parameter for the gelation behavior of the (DMA-DEGMA)x stars, the same as the DEA fraction was for the (DMA-DEA)x stars. Unexpectedly, the mechanical properties of these gels can also not be changed by heating above the transition temperature of PDMA at pH values around 8. The gels formed in this pH region are strong and too rigid to be affected, similar to strong gels formed from (DMA-DEA)x stars. Only when the pH is increased close to 9 and the subsequently formed gels are softer, a decrease in the moduli is observed.
We also quaternized the inner PDMA blocks of the (DMA-DEGMA)x stars to transform them it into strong polycations. This leads to an increase in the effective volume fraction of the stars and consequently to a significant decrease of the critical gelation concentration. The quaternization opens our concept up to the introduction of light sensitivity through multivalent counterions and the incorporation of nanoparticles.
