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Even though quite different in occurrence and consequences, from a modeling perspective many natural hazards share similar properties and challenges. Their complex nature as well as lacking knowledge about their driving forces and potential effects make their analysis demanding: uncertainty about the modeling framework, inaccurate or incomplete event observations and the intrinsic randomness of the natural phenomenon add up to different interacting layers of uncertainty, which require a careful handling. Nevertheless deterministic approaches are still widely used in natural hazard assessments, holding the risk of underestimating the hazard with disastrous effects. The all-round probabilistic framework of Bayesian networks constitutes an attractive alternative. In contrast to deterministic proceedings, it treats response variables as well as explanatory variables as random variables making no difference between input and output variables. Using a graphical representation Bayesian networks encode the dependency relations between the variables in a directed acyclic graph: variables are represented as nodes and (in-)dependencies between variables as (missing) edges between the nodes. The joint distribution of all variables can thus be described by decomposing it, according to the depicted independences, into a product of local conditional probability distributions, which are defined by the parameters of the Bayesian network. In the framework of this thesis the Bayesian network approach is applied to different natural hazard domains (i.e. seismic hazard, flood damage and landslide assessments). Learning the network structure and parameters from data, Bayesian networks reveal relevant dependency relations between the included variables and help to gain knowledge about the underlying processes. The problem of Bayesian network learning is cast in a Bayesian framework, considering the network structure and parameters as random variables itself and searching for the most likely combination of both, which corresponds to the maximum a posteriori (MAP score) of their joint distribution given the observed data. Although well studied in theory the learning of Bayesian networks based on real-world data is usually not straight forward and requires an adoption of existing algorithms. Typically arising problems are the handling of continuous variables, incomplete observations and the interaction of both. Working with continuous distributions requires assumptions about the allowed families of distributions. To "let the data speak" and avoid wrong assumptions, continuous variables are instead discretized here, thus allowing for a completely data-driven and distribution-free learning. An extension of the MAP score, considering the discretization as random variable as well, is developed for an automatic multivariate discretization, that takes interactions between the variables into account. The discretization process is nested into the network learning and requires several iterations. Having to face incomplete observations on top, this may pose a computational burden. Iterative proceedings for missing value estimation become quickly infeasible. A more efficient albeit approximate method is used instead, estimating the missing values based only on the observations of variables directly interacting with the missing variable. Moreover natural hazard assessments often have a primary interest in a certain target variable. The discretization learned for this variable does not always have the required resolution for a good prediction performance. Finer resolutions for (conditional) continuous distributions are achieved with continuous approximations subsequent to the Bayesian network learning, using kernel density estimations or mixtures of truncated exponential functions. All our proceedings are completely data-driven. We thus avoid assumptions that require expert knowledge and instead provide domain independent solutions, that are applicable not only in other natural hazard assessments, but in a variety of domains struggling with uncertainties.
The Prussian geologist Leopold von Buch was a lifelong friend of Alexander von Humboldt and had a significant influence on Humboldt’s geological ideas. In a talk, held in Berlin in 1831, which is published here for the first time, von Buch presented the Duria Antiquior of 1830 by the English geologist Henry De La Beche. The Duria Antiquior is widely regarded as the earliest depiction of a scene of prehistoric life from deep time. The print raised new questions about the processes of geohistorical change. The talk reveals that Leopold von Buch was a true scientist of the Romantic Age. His descriptions of geohistorical organismic transformations are taken from pictorial examples of organismic transformation from the classical literature. The talk also illustrates how influential English geologists were for geo-historical reconstructions in Germany.
It was the goal of this work to explore two different synthesis pathways using green chemistry. The first part of this thesis is focusing on the use of the urea-glass route towards single phase manganese nitride and manganese nitride/oxide nano-composites embedded in carbon, while the second part of the thesis is focusing on the use of the “saccharide route” (namely cellulose, sucrose, glucose and lignin) towards metal (Ni0), metal alloy (Pd0.9Ni0.1, Pd0.5Ni0.5, Fe0.5Ni0.5, Cu0.5Ni0.5 and W0.15Ni0.85) and ternary carbide (Mn0.75Fe2.25C) nanoparticles embedded in carbon. In the interest of battery application, MnN0.43 nanoparticles surrounded by a graphitic shell and embedded in carbon with a high surface area (79 m^2/g) were synthesized, following a previously set route.The comparison of the material characteristics before and after the discharge showed no remarkable difference in terms of composition and just slight differences in the morphological point of view, meaning the particles are stable but agglomerate. The graphitic shell is contributing to the resistance of the material and leads to a fine cyclic stability over 140 cycles of 230 mAh/g after the first charge/discharge and coulombic efficiencies close to 100%. Due to the low voltage towards Li/Li+ and the low polarization, it might be an attractive anode material for lithium ion batteries. However, the capacity is still noticeably lower than the theoretical value for MnN0.43. A mixture of MnN0.43 and MnO nanoparticles embedded in carbon (surface area 93 m^2/g) was able to improve the cyclic stability to over 160 cycles giving a capacity of 811 mAh/g, which is considerably higher than the capacity of the conventional material graphite (372 mAh/g). This nano-composite seems to agglomerate less during the process of discharge. Interestingly, although the capacity is much higher than of the single phase manganese nitride, the nano-composite seems to only contain MnN0.43 nanoparticles after the process of discharge with no oxide phase to be found. Concerning catalysis application, different metal, metal alloy, and metal carbide nanoparticles were synthesized using the saccharide route. At first, systems that were already investigated before, being Pd0.9Ni0.1, Pd0.5Ni0.5, Fe0.5Ni0.5 and Mn0.75Fe2.25C using cellulose as the carbon source were prepared and tested in an alkylation reaction of toluene with benzylchloride. Unexpectedly, the metal alloys did not show any catalytic activity, but the ternary carbide Mn0.75Fe2.25C showed fine catalytic activity of 98% conversion after 9 hour reaction time (110 °C). In a second step, the saccharide route was modified towards other carbon sources and carbon to metal ratios in order to improve the homogeneity of the samples and accessibility of the particle surfaces. The used carbon sources sucrose and glucose are similar in their basic structure of carbohydrates, but reducing the (polymeric) chain length. Indeed, the cellulose could be successfully replaced by sucrose and glucose. A lower carbon to metal ratio was found to influence the size, homogeneity and accessibility (as evidenced by TEM) of the samples. Since sucrose is an aliment, glucose is the better choice as a carbon source. Using glucose, the synthesis of Cu0.5Ni0.5 and W0.15Ni0.85 nano-composites was also possible, although the later was never obtained as pure phase. These alloy nano-composites were tested, along with nickel0 nanoparticles also prepared with glucose and on their catalytic activity towards the reduction of phenylacetylene. The results obtained let believe that any (poly) saccharide, including lignin, could be used as carbon source. The nickel0 nano-composites prepared with lignin as a carbon source were tested along with those prepared with cellulose and sucrose for their catalytic activity in the transfer hydrogenation of nitrobenzene (results compared with exposed nickel nanoparticles and nickel supported on carbon) leading to very promising results. Based on the urea-glass route and the saccharide route, simple equipment and transition metals, it was possible to have a one-pot synthesize with scale-up possibilities towards new material that can be applied in catalysis and battery systems.
In this work, thermosensitive hydrogels having tunable thermo-mechanical properties were synthesized. Generally the thermal transition of thermosensitive hydrogels is based on either a lower critical solution temperature (LCST) or critical micelle concentration/ temperature (CMC/ CMT). The temperature dependent transition from sol to gel with large volume change may be seen in the former type of thermosensitive hydrogels and is negligible in CMC/ CMT dependent systems. The change in volume leads to exclusion of water molecules, resulting in shrinking and stiffening of system above the transition temperature. The volume change can be undesired when cells are to be incorporated in the system. The gelation in the latter case is mainly driven by micelle formation above the transition temperature and further colloidal packing of micelles around the gelation temperature. As the gelation mainly depends on concentration of polymer, such a system could undergo fast dissolution upon addition of solvent. Here, it was envisioned to realize a thermosensitive gel based on two components, one responsible for a change in mechanical properties by formation of reversible netpoints upon heating without volume change, and second component conferring degradability on demand. As first component, an ABA triblockcopolymer (here: Poly(ethylene glycol)-b-poly(propylene glycol)-b-poly(ethylene glycol) (PEPE) with thermosensitive properties, whose sol-gel transition on the molecular level is based on micellization and colloidal jamming of the formed micelles was chosen, while for the additional macromolecular component crosslinking the formed micelles biopolymers were employed. The synthesis of the hydrogels was performed in two ways, either by physical mixing of compounds showing electrostatic interactions, or by covalent coupling of the components. Biopolymers (here: the polysaccharides hyaluronic acid, chondroitin sulphate, or pectin, as well as the protein gelatin) were employed as additional macromolecular crosslinker to simultaneously incorporate an enzyme responsiveness into the systems. In order to have strong ionic/electrostatic interactions between PEPE and polysaccharides, PEPE was aminated to yield predominantly mono- or di-substituted PEPEs. The systems based on aminated PEPE physically mixed with HA showed an enhancement in the mechanical properties such as, elastic modulus (G′) and viscous modulus (G′′) and a decrease of the gelation temperature (Tgel) compared to the PEPE at same concentration. Furthermore, by varying the amount of aminated PEPE in the composition, the Tgel of the system could be tailored to 27-36 °C. The physical mixtures of HA with di-amino PEPE (HA·di-PEPE) showed higher elastic moduli G′ and stability towards dissolution compared to the physical mixtures of HA with mono-amino PEPE (HA·mono-PEPE). This indicates a strong influence of electrostatic interaction between –COOH groups of HA and –NH2 groups of PEPE. The physical properties of HA with di-amino PEPE (HA·di-PEPE) compare beneficially with the physical properties of the human vitreous body, the systems are highly transparent, and have a comparable refractive index and viscosity. Therefore,this material was tested for a potential biological application and was shown to be non-cytotoxic in eluate and direct contact tests. The materials will in the future be investigated in further studies as vitreous body substitutes. In addition, enzymatic degradation of these hydrogels was performed using hyaluronidase to specifically degrade the HA. During the degradation of these hydrogels, increase in the Tgel was observed along with decrease in the mechanical properties. The aminated PEPE were further utilised in the covalent coupling to Pectin and chondroitin sulphate by using EDC as a coupling agent. Here, it was possible to adjust the Tgel (28-33 °C) by varying the grafting density of PEPE to the biopolymer. The grafting of PEPE to Pectin enhanced the thermal stability of the hydrogel. The Pec-g-PEPE hydrogels were degradable by enzymes with slight increase in Tgel and decrease in G′ during the degradation time. The covalent coupling of aminated PEPE to HA was performed by DMTMM as a coupling agent. This method of coupling was observed to be more efficient compared to EDC mediated coupling. Moreover, the purification of the final product was performed by ultrafiltration technique, which efficiently removed the unreacted PEPE from the final product, which was not sufficiently achieved by dialysis. Interestingly, the final products of these reaction were in a gel state and showed enhancement in the mechanical properties at very low concentrations (2.5 wt%) near body temperature. In these hydrogels the resulting increase in mechanical properties was due to the combined effect of micelle packing (physical interactions) by PEPE and covalent netpoints between PEPE and HA. PEPE alone or the physical mixtures of the same components were not able to show thermosensitive behavior at concentrations below 16 wt%. These thermosensitive hydrogels also showed on demand solubilisation by enzymatic degradation. The concept of thermosensitivity was introduced to 3D architectured porous hydrogels, by covalently grafting the PEPE to gelatin and crosslinking with LDI as a crosslinker. Here, the grafted PEPE resulted in a decrease in the helix formation in gelatin chains and after fixing the gelatin chains by crosslinking, the system showed an enhancement in the mechanical properties upon heating (34-42 °C) which was reversible upon cooling. A possible explanation of the reversible changes in mechanical properties is the strong physical interactions between micelles formed by PEPE being covalently linked to gelatin. Above the transition temperature, the local properties were evaluated by AFM indentation of pore walls in which an increase in elastic modulus (E) at higher temperature (37 °C) was observed. The water uptake of these thermosensitive architectured porous hydrogels was also influenced by PEPE and temperature (25 °C and 37 °C), showing lower water up take at higher temperature and vice versa. In addition, due to the lower water uptake at high temperature, the rate of hydrolytic degradation of these systems was found to be decreased when compared to pure gelatin architectured porous hydrogels. Such temperature sensitive architectured porous hydrogels could be important for e.g. stem cell culturing, cell differentiation and guided cell migration, etc. Altogether, it was possible to demonstrate that the crosslinking of micelles by a macromolecular crosslinker increased the shear moduli, viscosity, and stability towards dissolution of CMC-based gels. This effect could be likewise be realized by covalent or non-covalent mechanisms such as, micelle interactions, physical interactions of gelatin chains and physical interactions between gelatin chains and micelles. Moreover, the covalent grafting of PEPE will create additional net-points which also influence the mechanical properties of thermosensitive architectured porous hydrogels. Overall, the physical and chemical interactions and reversible physical interactions in such thermosensitive architectured porous hydrogels gave a control over the mechanical properties of such complex system. The hydrogels showing change of mechanical properties without a sol-gel transition or volume change are especially interesting for further study with cell proliferation and differentiation.
The surface heat flow (qs) is paramount for modeling the thermal structure of the lithosphere. Changes in the qs over a distinct lithospheric unit are normally directly reflecting changes in the crustal composition and therewith the radiogenic heat budget (e.g., Rudnick et al., 1998; Förster and Förster, 2000; Mareschal and Jaupart, 2004; Perry et al., 2006; Hasterok and Chapman, 2011, and references therein) or, less usual, changes in the mantle heat flow (e.g., Pollack and Chapman, 1977). Knowledge of this physical property is therefore of great interest for both academic research and the energy industry. The present study focuses on the qs of central and southern Israel as part of the Sinai Microplate (SM). Having formed during Oligocene to Miocene rifting and break-up of the African and Arabian plates, the SM is characterized by a young and complex tectonic history. Resulting from the time thermal diffusion needs to pass through the lithosphere, on the order of several tens-of-millions of years (e.g., Fowler, 1990); qs-values of the area reflect conditions of pre-Oligocene times. The thermal structure of the lithosphere beneath the SM in general, and south-central Israel in particular, has remained poorly understood. To address this problem, the two parameters needed for the qs determination were investigated. Temperature measurements were made at ten pre-existing oil and water exploration wells, and the thermal conductivity of 240 drill core and outcrop samples was measured in the lab. The thermal conductivity is the sensitive parameter in this determination. Lab measurements were performed on both, dry and water-saturated samples, which is labor- and time-consuming. Another possibility is the measurement of thermal conductivity in dry state and the conversion to a saturated value by using mean model approaches. The availability of a voluminous and diverse dataset of thermal conductivity values in this study allowed (1) in connection with the temperature gradient to calculate new reliable qs values and to use them to model the thermal pattern of the crust in south-central Israel, prior to young tectonic events, and (2) in connection with comparable datasets, controlling the quality of different mean model approaches for indirect determination of bulk thermal conductivity (BTC) of rocks. The reliability of numerically derived BTC values appears to vary between different mean models, and is also strongly dependent upon sample lithology. Yet, correction algorithms may significantly reduce the mismatch between measured and calculated conductivity values based on the different mean models. Furthermore, the dataset allowed the derivation of lithotype-specific conversion equations to calculate the water-saturated BTC directly from data of dry-measured BTC and porosity (e.g., well log derived porosity) with no use of any mean model and thus provide a suitable tool for fast analysis of large datasets. The results of the study indicate that the qs in the study area is significantly higher than previously assumed. The new presented qs values range between 50 and 62 mW m⁻². A weak trend of decreasing heat flow can be identified from the east to the west (55-50 mW m⁻²), and an increase from the Dead Sea Basin to the south (55-62 mW m⁻²). The observed range can be explained by variation in the composition (heat production) of the upper crust, accompanied by more systematic spatial changes in its thickness. The new qs data then can be used, in conjunction with petrophysical data and information on the structure and composition of the lithosphere, to adjust a model of the pre-Oligocene thermal state of the crust in south-central Israel. The 2-D steady-state temperature model was calculated along an E-W traverse based on the DESIRE seismic profile (Mechie et al., 2009). The model comprises the entire lithosphere down to the lithosphere–asthenosphere boundary (LAB) involving the most recent knowledge of the lithosphere in pre-Oligocene time, i.e., prior to the onset of rifting and plume-related lithospheric thermal perturbations. The adjustment of modeled and measured qs allows conclusions about the pre-Oligocene LAB-depth. After the best fitting the most likely depth is 150 km which is consistent with estimations made in comparable regions of the Arabian Shield. It therefore comprises the first ever modelled pre-Oligocene LAB depth, and provides important clues on the thermal state of lithosphere before rifting. This, in turn, is vital for a better understanding of the (thermo)-dynamic processes associated with lithosphere extension and continental break-up.
This cumulative dissertation explored the use of the detection of natural background of fast neutrons, the so-called cosmic-ray neutron sensing (CRS) approach to measure field-scale soil moisture in cropped fields. Primary cosmic rays penetrate the top atmosphere and interact with atmospheric particles. Such interaction results on a cascade of high-energy neutrons, which continue traveling through the atmospheric column. Finally, neutrons penetrate the soil surface and a second cascade is produced with the so-called secondary cosmic-ray neutrons (fast neutrons). Partly, fast neutrons are absorbed by hydrogen (soil moisture). Remaining neutrons scatter back to the atmosphere, where its flux is inversely correlated to the soil moisture content, therefore allowing a non-invasive indirect measurement of soil moisture. The CRS methodology is mainly evaluated based on a field study carried out on a farmland in Potsdam (Brandenburg, Germany) along three crop seasons with corn, sunflower and winter rye; a bare soil period; and two winter periods. Also, field monitoring was carried out in the Schaefertal catchment (Harz, Germany) for long-term testing of CRS against ancillary data. In the first experimental site, the CRS method was calibrated and validated using different approaches of soil moisture measurements. In a period with corn, soil moisture measurement at the local scale was performed at near-surface only, and in subsequent periods (sunflower and winter rye) sensors were placed in three depths (5 cm, 20 cm and 40 cm). The direct transfer of CRS calibration parameters between two vegetation periods led to a large overestimation of soil moisture by the CRS. Part of this soil moisture overestimation was attributed to an underestimation of the CRS observation depth during the corn period ( 5-10 cm), which was later recalculated to values between 20-40 cm in other crop periods (sunflower and winter rye). According to results from these monitoring periods with different crops, vegetation played an important role on the CRS measurements. Water contained also in crop biomass, above and below ground, produces important neutron moderation. This effect was accounted for by a simple model for neutron corrections due to vegetation. It followed crop development and reduced overall CRS soil moisture error for periods of sunflower and winter rye. In Potsdam farmland also inversely-estimated soil hydraulic parameters were determined at the field scale, using CRS soil moisture from the sunflower period. A modelling framework coupling HYDRUS-1D and PEST was applied. Subsequently, field-scale soil hydraulic properties were compared against local scale soil properties (modelling and measurements). Successful results were obtained here, despite large difference in support volume. Simple modelling framework emphasizes future research directions with CRS soil moisture to parameterize field scale models. In Schaefertal catchment, CRS measurements were verified using precipitation and evapotranspiration data. At the monthly resolution, CRS soil water storage was well correlated to these two weather variables. Also clearly, water balance could not be closed due to missing information from other compartments such as groundwater, catchment discharge, etc. In the catchment, the snow influence to natural neutrons was also evaluated. As also observed in Potsdam farmland, CRS signal was strongly influenced by snow fall and snow accumulation. A simple strategy to measure snow was presented for Schaefertal case. Concluding remarks of this dissertation showed that (a) the cosmic-ray neutron sensing (CRS) has a strong potential to provide feasible measurement of mean soil moisture at the field scale in cropped fields; (b) CRS soil moisture is strongly influenced by other environmental water pools such as vegetation and snow, therefore these should be considered in analysis; (c) CRS water storage can be used for soil hydrology modelling for determination of soil hydraulic parameters; and (d) CRS approach has strong potential for long term monitoring of soil moisture and for addressing studies of water balance.
The sharply rising level of atmospheric carbon dioxide resulting from anthropogenic emissions is one of the greatest environmental concerns facing our civilization today. Metal-organic frameworks (MOFs) are a new class of materials that constructed by metal-containing nodes bonded to organic bridging ligands. MOFs could serve as an ideal platform for the development of next generation CO2 capture materials owing to their large capacity for the adsorption of gases and their structural and chemical tunability. The ability to rationally select the framework components is expected to allow the affinity of the internal pore surface toward CO2 to be precisely controlled, facilitating materials properties that are optimized for the specific type of CO2 capture to be performed (post-combustion capture, precombustion capture, or oxy-fuel combustion) and potentially even for the specific power plant in which the capture system is to be installed. For this reason, significant effort has been made in recent years in improving the gas separation performance of MOFs and some studies evaluating the prospects of deploying these materials in real-world CO2 capture systems have begun to emerge. We have developed six new MOFs, denoted as IFPs (IFP-5, -6, -7, -8, -9, -10, IFP = Imidazolate Framework Potsdam) and two hydrogen-bonded molecular building block (MBB, named as 1 and 2 for Zn and Co based, respectively) have been synthesized, characterized and applied for gas storage. The structure of IFP possesses 1D hexagonal channels. Metal centre and the substituent groups of C2 position of the linker protrude into the open channels and determine their accessible diameter. Interestingly, the channel diameters (range : 0.3 to 5.2 Å) for IFP structures are tuned by the metal centre (Zn, Co and Cd) and substituent of C2 position of the imidazolate linker. Moreover hydrogen bonded MBB of 1 and 2 is formed an in situ functionalization of a ligand under solvothermal condition. Two different types of channels are observed for 1 and 2. Materials contain solvent accessible void space. Solvent could be easily removed by under high vacuum. The porous framework has maintained the crystalline integrity even without solvent molecules. N2, H2, CO2 and CH4 gas sorption isotherms were performed. Gas uptake capacities are comparable with other frameworks. Gas uptake capacity is reduced when the channel diameter is narrow. For example, the channel diameter of IFP-5 (channel diameter: 3.8 Å) is slightly lower than that of IFP-1 (channel diameter: 4.2 Å); hence, the gas uptake capacity and Brunauer-Emmett-Teller (BET) surface area are slightly lower than IFP-1. The selectivity does not depend only on the size of the gas components (kinetic diameter: CO2 3.3 Å, N2 3.6 Å and CH4 3.8 ) but also on the polarizability of the surface and of the gas components. IFP-5 and-6 have the potential applications for the separation of CO2 and CH4 from N2-containing gas mixtures and CO2 and CH4 containing gas mixtures. Gas sorption isotherms of IFP-7, -8, -9, -10 exhibited hysteretic behavior due to flexible alkoxy (e.g., methoxy and ethoxy) substituents. Such phenomenon is a kind of gate effects which is rarely observed in microporous MOFs. IFP-7 (Zn-centred) has a flexible methoxy substituent. This is the first example where a flexible methoxy substituent shows the gate opening behavior in a MOF. Presence of methoxy functional group at the hexagonal channels, IFP-7 acted as molecular gate for N2 gas. Due to polar methoxy group and channel walls, wide hysteretic isotherm was observed during gas uptake. The N2 The estimated BET surface area for 1 is 471 m2 g-1 and the Langmuir surface area is 570 m2 g-1. However, such surface area is slightly higher than azolate-based hydrogen-bonded supramolecular assemblies and also comparable and higher than some hydrogen-bonded porous organic molecules.
This thesis deals with Einstein metrics and the Ricci flow on compact mani- folds. We study the second variation of the Einstein-Hilbert functional on Ein- stein metrics. In the first part of the work, we find curvature conditions which ensure the stability of Einstein manifolds with respect to the Einstein-Hilbert functional, i.e. that the second variation of the Einstein-Hilbert functional at the metric is nonpositive in the direction of transverse-traceless tensors. The second part of the work is devoted to the study of the Ricci flow and how its behaviour close to Einstein metrics is influenced by the variational be- haviour of the Einstein-Hilbert functional. We find conditions which imply that Einstein metrics are dynamically stable or unstable with respect to the Ricci flow and we express these conditions in terms of stability properties of the metric with respect to the Einstein-Hilbert functional and properties of the Laplacian spectrum.
The problem under consideration in the thesis is a two level atom in a photonic crystal and a pumping laser. The photonic crystal provides an environment for the atom, that modifies the decay of the exited state, especially if the atom frequency is close to the band gap. The population inversion is investigated als well as the emission spectrum. The dynamics is analysed in the context of open quantum systems. Due to the multiple reflections in the photonic crystal, the system has a finite memory that inhibits the Markovian approximation. In the Heisenberg picture the equations of motion for the system variables form a infinite hierarchy of integro-differential equations. To get a closed system, approximations like a weak coupling approximation are needed. The thesis starts with a simple photonic crystal that is amenable to analytic calculations: a one-dimensional photonic crystal, that consists of alternating layers. The Bloch modes inside and the vacuum modes outside a finite crystal are linked with a transformation matrix that is interpreted as a transfer matrix. Formulas for the band structure, the reflection from a semi-infinite crystal, and the local density of states in absorbing crystals are found; defect modes and negative refraction are discussed. The quantum optics section of the work starts with the discussion of three problems, that are related to the full resonance fluorescence problem: a pure dephasing model, the driven atom and resonance fluorescence in free space. In the lowest order of the system-environment coupling, the one-time expectation values for the full problem are calculated analytically and the stationary states are discussed for certain cases. For the calculation of the two time correlation functions and spectra, the additional problem of correlations between the two times appears. In the Markovian case, the quantum regression theorem is valid. In the general case, the fluctuation dissipation theorem can be used instead. The two-time correlation functions are calculated by the two different methods. Within the chosen approximations, both methods deliver the same result. Several plots show the dependence of the spectrum on the parameters. Some examples for squeezing spectra are shown with different approximations. A projection operator method is used to establish two kinds of Markovian expansion with and without time convolution. The lowest order is identical with the lowest order of system environment coupling, but higher orders give different results.
Learning a model for the relationship between the attributes and the annotated labels of data examples serves two purposes. Firstly, it enables the prediction of the label for examples without annotation. Secondly, the parameters of the model can provide useful insights into the structure of the data. If the data has an inherent partitioned structure, it is natural to mirror this structure in the model. Such mixture models predict by combining the individual predictions generated by the mixture components which correspond to the partitions in the data. Often the partitioned structure is latent, and has to be inferred when learning the mixture model. Directly evaluating the accuracy of the inferred partition structure is, in many cases, impossible because the ground truth cannot be obtained for comparison. However it can be assessed indirectly by measuring the prediction accuracy of the mixture model that arises from it. This thesis addresses the interplay between the improvement of predictive accuracy by uncovering latent cluster structure in data, and further addresses the validation of the estimated structure by measuring the accuracy of the resulting predictive model. In the application of filtering unsolicited emails, the emails in the training set are latently clustered into advertisement campaigns. Uncovering this latent structure allows filtering of future emails with very low false positive rates. In order to model the cluster structure, a Bayesian clustering model for dependent binary features is developed in this thesis. Knowing the clustering of emails into campaigns can also aid in uncovering which emails have been sent on behalf of the same network of captured hosts, so-called botnets. This association of emails to networks is another layer of latent clustering. Uncovering this latent structure allows service providers to further increase the accuracy of email filtering and to effectively defend against distributed denial-of-service attacks. To this end, a discriminative clustering model is derived in this thesis that is based on the graph of observed emails. The partitionings inferred using this model are evaluated through their capacity to predict the campaigns of new emails. Furthermore, when classifying the content of emails, statistical information about the sending server can be valuable. Learning a model that is able to make use of it requires training data that includes server statistics. In order to also use training data where the server statistics are missing, a model that is a mixture over potentially all substitutions thereof is developed. Another application is to predict the navigation behavior of the users of a website. Here, there is no a priori partitioning of the users into clusters, but to understand different usage scenarios and design different layouts for them, imposing a partitioning is necessary. The presented approach simultaneously optimizes the discriminative as well as the predictive power of the clusters. Each model is evaluated on real-world data and compared to baseline methods. The results show that explicitly modeling the assumptions about the latent cluster structure leads to improved predictions compared to the baselines. It is beneficial to incorporate a small number of hyperparameters that can be tuned to yield the best predictions in cases where the prediction accuracy can not be optimized directly.