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The immense popularity of online communication services in the last decade has not only upended our lives (with news spreading like wildfire on the Web, presidents announcing their decisions on Twitter, and the outcome of political elections being determined on Facebook) but also dramatically increased the amount of data exchanged on these platforms. Therefore, if we wish to understand the needs of modern society better and want to protect it from new threats, we urgently need more robust, higher-quality natural language processing (NLP) applications that can recognize such necessities and menaces automatically, by analyzing uncensored texts. Unfortunately, most NLP programs today have been created for standard language, as we know it from newspapers, or, in the best case, adapted to the specifics of English social media.
This thesis reduces the existing deficit by entering the new frontier of German online communication and addressing one of its most prolific forms—users’ conversations on Twitter. In particular, it explores the ways and means by how people express their opinions on this service, examines current approaches to automatic mining of these feelings, and proposes novel methods, which outperform state-of-the-art techniques. For this purpose, I introduce a new corpus of German tweets that have been manually annotated with sentiments, their targets and holders, as well as lexical polarity items and their contextual modifiers. Using these data, I explore four major areas of sentiment research: (i) generation of sentiment lexicons, (ii) fine-grained opinion mining, (iii) message-level polarity classification, and (iv) discourse-aware sentiment analysis. In the first task, I compare three popular groups of lexicon generation methods: dictionary-, corpus-, and word-embedding–based ones, finding that dictionary-based systems generally yield better polarity lists than the last two groups. Apart from this, I propose a linear projection algorithm, whose results surpass many existing automatically-generated lexicons. Afterwords, in the second task, I examine two common approaches to automatic prediction of sentiment spans, their sources, and targets: conditional random fields (CRFs) and recurrent neural networks, obtaining higher scores with the former model and improving these results even further by redefining the structure of CRF graphs. When dealing with message-level polarity classification, I juxtapose three major sentiment paradigms: lexicon-, machine-learning–, and deep-learning–based systems, and try to unite the first and last of these method groups by introducing a bidirectional neural network with lexicon-based attention. Finally, in order to make the new classifier aware of microblogs' discourse structure, I let it separately analyze the elementary discourse units of each tweet and infer the overall polarity of a message from the scores of its EDUs with the help of two new approaches: latent-marginalized CRFs and Recursive Dirichlet Process.
There is evidence that infants start extracting words from fluent speech around 7.5 months of age (e.g., Jusczyk & Aslin, 1995) and that they use at least two mechanisms to segment words forms from fluent speech: prosodic information (e.g., Jusczyk, Cutler & Redanz, 1993) and statistical information (e.g., Saffran, Aslin & Newport, 1996). However, how these two mechanisms interact and whether they change during development is still not fully understood.
The main aim of the present work is to understand in what way different cues to word segmentation are exploited by infants when learning the language in their environment, as well as to explore whether this ability is related to later language skills. In Chapter 3 we pursued to determine the reliability of the method used in most of the experiments in the present thesis (the Headturn Preference Procedure), as well as to examine correlations and individual differences between infants’ performance and later language outcomes. In Chapter 4 we investigated how German-speaking adults weigh statistical and prosodic information for word segmentation. We familiarized adults with an auditory string in which statistical and prosodic information indicated different word boundaries and obtained both behavioral and pupillometry responses. Then, we conducted further experiments to understand in what way different cues to word segmentation are exploited by 9-month-old German-learning infants (Chapter 5) and by 6-month-old German-learning infants (Chapter 6). In addition, we conducted follow-up questionnaires with the infants and obtained language outcomes at later stages of development.
Our findings from this thesis revealed that (1) German-speaking adults show a strong weight of prosodic cues, at least for the materials used in this study and that (2) German-learning infants weight these two kind of cues differently depending on age and/or language experience. We observed that, unlike English-learning infants, 6-month-old infants relied more strongly on prosodic cues. Nine-month-olds do not show any preference for either of the cues in the word segmentation task. From the present results it remains unclear whether the ability to use prosodic cues to word segmentation relates to later language vocabulary. We speculate that prosody provides infants with their first window into the specific acoustic regularities in the signal, which enables them to master the specific stress pattern of German rapidly. Our findings are a step forwards in the understanding of an early impact of the native prosody compared to statistical learning in early word segmentation.
Species assembly from a regional pool into local metacommunities and how they colonize and coexist over time and space is essential to understand how communities response to their environment including abiotic and biotic factors. In highly disturbed landscapes, connectivity of isolated habitat patches is essential to maintain biodiversity and the entire ecosystem functioning. In northeast Germany, a high density of the small water bodies called kettle holes, are good systems to study metacommunities due to their condition as “aquatic islands” suitable for hygrophilous species that are surrounded by in unsuitable matrix of crop fields. The main objective of this thesis was to infer the main ecological processes shaping plant communities and their response to the environment, from biodiversity patterns and key life-history traits involved in connectivity using ecological and genetic approaches; and to provide first insights of the role of kettle holes harboring wild-bee species as important mobile linkers connecting plant communities in this insular system.
t a community level, I compared plant diversity patterns and trait composition in ephemeral vs. permanent kettle holes). My results showed that types of kettle holes act as environmental filers shaping plant diversity, community-composition and trait-distribution, suggesting species sorting and niche processes in both types of kettle holes. At a population level, I further analyzed the role of dispersal and reproductive strategies of four selected species occurring in permanent kettle holes. Using microsatellites, I found that breeding system (degree of clonality), is the main factor shaping genetic diversity and genetic divergence. Although, higher gene flow and lower genetic differentiation among populations in wind vs. insect pollinated species was also found, suggesting that dispersal mechanisms played a role related to gene flow and connectivity. For most flowering plants, pollinators play an important role connecting communities. Therefore, as a first insight of the potential mobile linkers of these plant communities, I investigated the diversity wild-bees occurring in these kettle holes. My main results showed that local habitat quality (flower resources) had a positive effect on bee diversity, while habitat heterogeneity (number of natural landscape elements surrounding kettle holes 100–300m), was negatively correlated.
This thesis covers from genetic flow at individual and population level to plant community assembly. My results showed how patterns of biodiversity, dispersal and reproduction strategies in plant population and communities can be used to infer ecological processes. In addition, I showed the importance of life-history traits and the relationship between species and their abiotic and biotic interactions. Furthermore, I included a different level of mobile linkers (pollinators) for a better understanding of another level of the system. This integration is essential to understand how communities respond to their surrounding environment and how disturbances such as agriculture, land-use and climate change might affect them. I highlight the need to integrate many scientific areas covering from genes to ecosystems at different spatiotemporal scales for a better understanding, management and conservation of our ecosystems.
Die Wissenschaftsfreiheit ist ein Grundrecht, dessen Sinn und Auslegung im Rahmen von Reformen des Hochschulsystems nicht nur der Justiz, sondern auch der Wissenschaft selbst immer wieder Anlass zur Diskussion geben, so auch im Zuge der Einführung des so genannten Qualitätsmanagements von Studium und Lehre an deutschen Hochschulen. Die vorliegende Dissertationsschrift stellt die Ergebnisse einer empirischen Studie vor, die mit einer soziologischen Betrachtung des Qualitätsmanagements unterschiedlicher Hochschulen zu dieser Diskussion beiträgt.
Auf Grundlage der Prämisse, dass Verlauf und Folgen einer organisationalen Innovation nur verstanden werden können, wenn der alltägliche Umgang der Organisationsmitglieder mit den neuen Strukturen und Prozessen in die Analyse einbezogen wird, geht die Studie von der Frage aus, wie Akteurinnen und Akteure an deutschen Hochschulen die Qualitätsmanagementsysteme ihrer Organisationen nutzen. Die qualitative inhaltsanalytische Auswertung von 26 Leitfaden-Interviews mit Prorektorinnen und -rektoren, Qualitätsmanagement-Personal und Studiendekaninnen und -dekanen an neun Hochschulen ergibt, dass die Strategien der Akteursgruppen an den Hochschulen im Zusammenspiel mit strukturellen Aspekten unterschiedliche Dynamiken entstehen lassen, mit denen Implikationen für die Lehrfreiheit verbunden sind: Während die Autonomie der Lehrenden durch das Qualitätsmanagement an einigen Hochschulen unterstützt wird, sind sowohl Autonomie als auch Verantwortung für Studium und Lehre an anderen Hochschulen Gegenstand andauernder Konflikte, die auch das Qualitätsmanagement einschließen.
Water is essential to life and thus, an essential resource. However, freshwater resources are limited and their maintenance is crucial. Pollution with chemicals and pathogens through urbanization and a growing population impair the quality of freshwater. Furthermore, water can serve as vector for the transmission of pathogens resulting in water-borne illness.
The Interdisciplinary Research Group III – "Water" of the Leibniz alliance project INFECTIONS‘21 investigated water as a hub for pathogens focusing on Clostridioides difficile and avian influenza A viruses that may be shed into the water. Another aim of this study was to characterize the bacterial communities in a wastewater treatment plant (WWTP) of the capital Berlin, Germany to further assess potential health risks associated with wastewater management practices.
Bacterial communities of WWTP inflow and effluent differed significantly. The proportion of fecal/enteric bacteria was relatively low and OTUs related to potential enteric pathogens were largely removed from inflow to effluent. However, a health risk might exist as an increased relative abundance of potential pathogenic Legionella spp. such as L. lytica was observed. Three Clostridioides difficile isolates from wastewater inflow and an urban bathing lake in Berlin (‗Weisser See‘) were obtained and sequenced. The two isolates from the wastewater did not carry toxin genes, whereas the isolate from the lake was positive for the toxin genes. All three isolates were closely related to human strains. This indicates a potential, but rather sporadic health risk. Avian influenza A viruses were detected in 38.8% of sediment samples by PCR, but virus isolation failed. An experiment with inoculated freshwater and sediment samples showed that virus isolation from sediment requires relatively high virus concentrations and worked much better in Madin-Darby Canine Kidney (MDCK) cell cultures than in embryonated chicken eggs, but low titre of influenza contamination in freshwater samples was sufficient to recover virus.
In conclusion, this work revealed potential health risks coming from bacterial groups with pathogenic potential such as Legionella spp. whose relative abundance is higher in the released effluent than in the inflow of the investigated WWTP. It further indicates that water bodies such as wastewater and lake sediments can serve as reservoir and vector, even for non-typical water-borne or water-transmitted pathogens such as C. difficile.
Supermassive black holes reside in the hearts of almost all massive galaxies. Their evolutionary path seems to be strongly linked to the evolution of their host galaxies, as implied by several empirical relations between the black hole mass (M BH ) and different host galaxy properties. The physical driver of this co-evolution is, however, still not understood. More mass measurements over homogeneous samples and a detailed understanding of systematic uncertainties are required to fathom the origin of the scaling relations.
In this thesis, I present the mass estimations of supermassive black holes in the nuclei of one late-type and thirteen early-type galaxies. Our SMASHING sample extends from the intermediate to the massive galaxy mass regime and was selected to fill in gaps in number of galaxies along the scaling relations. All galaxies were observed at high spatial resolution, making use of the adaptive-optics mode of integral field unit (IFU) instruments on state-of-the-art telescopes (SINFONI, NIFS, MUSE). I extracted the stellar kinematics from these observations and constructed dynamical Jeans and Schwarzschild models to estimate the mass of the central black holes robustly. My new mass estimates increase the number of early-type galaxies with measured black hole masses by 15%. The seven measured galaxies with nuclear light deficits (’cores’) augment the sample of cored galaxies with measured black holes by 40%. Next to determining massive black hole masses, evaluating the accuracy of black hole masses is crucial for understanding the intrinsic scatter of the black hole- host galaxy scaling relations. I tested various sources of systematic uncertainty on my derived mass estimates.
The M BH estimate of the single late-type galaxy of the sample yielded an upper limit, which I could constrain very robustly. I tested the effects of dust, mass-to-light ratio (M/L) variation, and dark matter on my measured M BH . Based on these tests, the typically assumed constant M/L ratio can be an adequate assumption to account for the small amounts of dark matter in the center of that galaxy. I also tested the effect of a variable M/L variation on the M BH measurement on a second galaxy. By considering stellar M/L variations in the dynamical modeling, the measured M BH decreased by 30%. In the future, this test should be performed on additional galaxies to learn how an as constant assumed M/L flaws the estimated black hole masses.
Based on our upper limit mass measurement, I confirm previous suggestions that resolving the predicted BH sphere-of-influence is not a strict condition to measure black hole masses. Instead, it is only a rough guide for the detection of the black hole if high-quality, and high signal-to-noise IFU data are used for the measurement. About half of our sample consists of massive early-type galaxies which show nuclear surface brightness cores and signs of triaxiality. While these types of galaxies are typically modeled with axisymmetric modeling methods, the effects on M BH are not well studied yet. The massive galaxies of our presented galaxy sample are well suited to test the effect of different stellar dynamical models on the measured black hole mass in evidently triaxial galaxies. I have compared spherical Jeans and axisymmetric Schwarzschild models and will add triaxial Schwarzschild models to this comparison in the future. The constructed Jeans and Schwarzschild models mostly disagree with each other and cannot reproduce many of the triaxial features of the galaxies (e.g., nuclear sub-components, prolate rotation). The consequence of the axisymmetric-triaxial assumption on the accuracy of M BH and its impact on the black hole - host galaxy relation needs to be carefully examined in the future.
In the sample of galaxies with published M BH , we find measurements based on different dynamical tracers, requiring different observations, assumptions, and methods. Crucially, different tracers do not always give consistent results. I have used two independent tracers (cold molecular gas and stars) to estimate M BH in a regular galaxy of our sample. While the two estimates are consistent within their errors, the stellar-based measurement is twice as high as the gas-based. Similar trends have also been found in the literature. Therefore, a rigorous test of the systematics associated with the different modeling methods is required in the future. I caution to take the effects of different tracers (and methods) into account when discussing the scaling relations.
I conclude this thesis by comparing my galaxy sample with the compilation of galaxies with measured black holes from the literature, also adding six SMASHING galaxies, which were published outside of this thesis. None of the SMASHING galaxies deviates significantly from the literature measurements. Their inclusion to the published early-type galaxies causes a change towards a shallower slope for the M BH - effective velocity dispersion relation, which is mainly driven by the massive galaxies of our sample. More unbiased and homogenous measurements are needed in the future to determine the shape of the relation and understand its physical origin.
Business process management is an established technique for business organizations to manage and support their processes. Those processes are typically represented by graphical models designed with modeling languages, such as the Business Process Model and Notation (BPMN).
Since process models do not only serve the purpose of documentation but are also a basis for implementation and automation of the processes, they have to satisfy certain correctness requirements. In this regard, the notion of soundness of workflow nets was developed, that can be applied to BPMN process models in order to verify their correctness. Because the original soundness criteria are very restrictive regarding the behavior of the model, different variants of the soundness notion have been developed for situations in which certain violations are not even harmful.
All of those notions do only consider the control-flow structure of a process model, however. This poses a problem, taking into account the fact that with the recent release and the ongoing development of the Decision Model and Notation (DMN) standard, an increasing number of process models are complemented by respective decision models. DMN is a dedicated modeling language for decision logic and separates the concerns of process and decision logic into two different models, process and decision models respectively.
Hence, this thesis is concerned with the development of decisionaware soundness notions, i.e., notions of soundness that build upon the original soundness ideas for process models, but additionally take into account complementary decision models. Similar to the various notions of workflow net soundness, this thesis investigates different notions of decision soundness that can be applied depending on the desired degree of restrictiveness. Since decision tables are a standardized means of DMN to represent decision logic, this thesis also puts special focus on decision tables, discussing how they can be translated into an unambiguous format and how their possible output values can be efficiently determined.
Moreover, a prototypical implementation is described that supports checking a basic version of decision soundness. The decision soundness notions were also empirically evaluated on models from participants of an online course on process and decision modeling as well as from a process management project of a large insurance company. The evaluation demonstrates that violations of decision soundness indeed occur and can be detected with our approach.
The Himalayas are a region that is most dependent, but also frequently prone to hazards from changing meltwater resources. This mountain belt hosts the highest mountain peaks on earth, has the largest reserve of ice outside the polar regions, and is home to a rapidly growing population in recent decades. One source of hazard has attracted scientific research in particular in the past two decades: glacial lake outburst floods (GLOFs) occurred rarely, but mostly with fatal and catastrophic consequences for downstream communities and infrastructure. Such GLOFs can suddenly release several million cubic meters of water from naturally impounded meltwater lakes. Glacial lakes have grown in number and size by ongoing glacial mass losses in the Himalayas. Theory holds that enhanced meltwater production may increase GLOF frequency, but has never been tested so far. The key challenge to test this notion are the high altitudes of >4000 m, at which lakes occur, making field work impractical. Moreover, flood waves can attenuate rapidly in mountain channels downstream, so that many GLOFs have likely gone unnoticed in past decades. Our knowledge on GLOFs is hence likely biased towards larger, destructive cases, which challenges a detailed quantification of their frequency and their response to atmospheric warming. Robustly quantifying the magnitude and frequency of GLOFs is essential for risk assessment and management along mountain rivers, not least to implement their return periods in building design codes.
Motivated by this limited knowledge of GLOF frequency and hazard, I developed an algorithm that efficiently detects GLOFs from satellite images. In essence, this algorithm classifies land cover in 30 years (~1988–2017) of continuously recorded Landsat images over the Himalayas, and calculates likelihoods for rapidly shrinking water bodies in the stack of land cover images. I visually assessed such detected tell-tale sites for sediment fans in the river channel downstream, a second key diagnostic of GLOFs. Rigorous tests and validation with known cases from roughly 10% of the Himalayas suggested that this algorithm is robust against frequent image noise, and hence capable to identify previously unknown GLOFs. Extending the search radius to the entire Himalayan mountain range revealed some 22 newly detected GLOFs. I thus more than doubled the existing GLOF count from 16 previously known cases since 1988, and found a dominant cluster of GLOFs in the Central and Eastern Himalayas (Bhutan and Eastern Nepal), compared to the rarer affected ranges in the North. Yet, the total of 38 GLOFs showed no change in the annual frequency, so that the activity of GLOFs per unit glacial lake area has decreased in the past 30 years. I discussed possible drivers for this finding, but left a further attribution to distinct GLOF-triggering mechanisms open to future research.
This updated GLOF frequency was the key input for assessing GLOF hazard for the entire Himalayan mountain belt and several subregions. I used standard definitions in flood hydrology, describing hazard as the annual exceedance probability of a given flood peak discharge [m3 s-1] or larger at the breach location. I coupled the empirical frequency of GLOFs per region to simulations of physically plausible peak discharges from all existing ~5,000 lakes in the Himalayas. Using an extreme-value model, I could hence calculate flood return periods. I found that the contemporary 100-year GLOF discharge (the flood level that is reached or exceeded on average once in 100 years) is 20,600+2,200/–2,300 m3 s-1 for the entire Himalayas. Given the spatial and temporal distribution of historic GLOFs, contemporary GLOF hazard is highest in the Eastern Himalayas, and lower for regions with rarer GLOF abundance. I also calculated GLOF hazard for some 9,500 overdeepenings, which could expose and fill with water, if all Himalayan glaciers have melted eventually. Assuming that the current GLOF rate remains unchanged, the 100-year GLOF discharge could double (41,700+5,500/–4,700 m3 s-1), while the regional GLOF hazard may increase largest in the Karakoram.
To conclude, these three stages–from GLOF detection, to analysing their frequency and estimating regional GLOF hazard–provide a framework for modern GLOF hazard assessment. Given the rapidly growing population, infrastructure, and hydropower projects in the Himalayas, this thesis assists in quantifying the purely climate-driven contribution to hazard and risk from GLOFs.
Thermoresponsive Zellkultursubstrate für zeitlich-räumlich gesteuertes Auswachsen neuronaler Zellen
(2019)
Ein wichtiges Ziel der Neurowissenschaften ist das Verständnis der komplexen und zugleich faszinierenden, hochgeordneten Vernetzung der Neurone im Gehirn, welche neuronalen Prozessen, wie zum Beispiel dem Wahrnehmen oder Lernen wie auch Neuropathologien zu Grunde liegt. Für verbesserte neuronale Zellkulturmodelle zur detaillierten Untersuchung dieser Prozesse ist daher die Rekonstruktion von geordneten neuronalen Verbindungen dringend erforderlich. Mit Oberflächenstrukturen aus zellattraktiven und zellabweisenden Beschichtungen können neuronale Zellen und ihre Neuriten in vitro strukturiert werden. Zur Kontrolle der neuronalen Verbindungsrichtung muss das Auswachsen der Axone zu benachbarten Zellen dynamisch gesteuert werden, zum Beispiel über eine veränderliche Zugänglichkeit der Oberfläche.
In dieser Arbeit wurde untersucht, ob mit thermoresponsiven Polymeren (TRP) beschichtete Zellkultursubstrate für eine dynamische Kontrolle des Auswachsens neuronaler Zellen geeignet sind. TRP können über die Temperatur von einem zellabweisenden in einen zellattraktiven Zustand geschaltet werden, womit die Zugänglichkeit der Oberfläche für Zellen dynamisch gesteuert werden kann. Die TRP-Beschichtung wurde mikrostrukturiert, um einzelne oder wenige neuronale Zellen zunächst auf der Oberfläche anzuordnen und das Auswachsen der Zellen und Neuriten über definierte TRP-Bereiche in Abhängigkeit der Temperatur zeitlich und räumlich zu kontrollieren. Das Protokoll wurde mit der neuronalen Zelllinie SH-SY5Y etabliert und auf humane induzierte Neurone übertragen. Die Anordnung der Zellen konnte bei Kultivierung im zellabweisenden Zustand des TRPs für bis zu 7 Tage aufrecht erhalten werden. Durch Schalten des TRPs in den zellattraktiven Zustand konnte das Auswachsen der Neuriten und Zellen zeitlich und räumlich induziert werden. Immunozytochemische Färbungen und Patch-Clamp-Ableitungen der Neurone demonstrierten die einfache Anwendbarkeit und Zellkompatibilität der TRP-Substrate.
Eine präzisere räumliche Kontrolle des Auswachsens der Zellen sollte durch lokales Schalten der TRP-Beschichtung erreicht werden. Dafür wurden Mikroheizchips mit Mikroelektroden zur lokalen Jouleschen Erwärmung der Substratoberfläche entwickelt. Zur Evaluierung der generierten Temperaturprofile wurde eine Temperaturmessmethode entwickelt und die erhobenen Messwerte mit numerisch simulierten Werten abgeglichen. Die Temperaturmessmethode basiert auf einfach zu applizierenden Sol-Gel-Schichten, die den temperatursensitiven Fluoreszenzfarbstoff Rhodamin B enthalten. Sie ermöglicht oberflächennahe Temperaturmessungen in trockener und wässriger Umgebung mit hoher Orts- und Temperaturauflösung. Numerische Simulationen der Temperaturprofile korrelierten gut mit den experimentellen Daten. Auf dieser Basis konnten Geometrie und Material der Mikroelektroden hinsichtlich einer lokal stark begrenzten Temperierung optimiert werden. Ferner wurden für die Kultvierung der Zellen auf den Mikroheizchips eine Zellkulturkammer und Kontaktboard für die elektrische Kontaktierung der Mikroelektroden geschaffen.
Die vorgestellten Ergebnisse demonstrieren erstmalig das enorme Potential thermoresponsiver Zellkultursubstrate für die zeitlich und räumlich gesteuerte Formation geordneter neuronaler Verbindungen in vitro. Zukünftig könnte dies detaillierte Studien zur neuronalen Informationsverarbeitung oder zu Neuropathologien an relevanten, humanen Zellmodellen ermöglichen.
Data assimilation has been an active area of research in recent years, owing to its wide utility. At the core of data assimilation are filtering, prediction, and smoothing procedures. Filtering entails incorporation of measurements' information into the model to gain more insight into a given state governed by a noisy state space model. Most natural laws are governed by time-continuous nonlinear models. For the most part, the knowledge available about a model is incomplete; and hence uncertainties are approximated by means of probabilities. Time-continuous filtering, therefore, holds promise for wider usefulness, for it offers a means of combining noisy measurements with imperfect model to provide more insight on a given state.
The solution to time-continuous nonlinear Gaussian filtering problem is provided for by the Kushner-Stratonovich equation. Unfortunately, the Kushner-Stratonovich equation lacks a closed-form solution. Moreover, the numerical approximations based on Taylor expansion above third order are fraught with computational complications. For this reason, numerical methods based on Monte Carlo methods have been resorted to. Chief among these methods are sequential Monte-Carlo methods (or particle filters), for they allow for online assimilation of data. Particle filters are not without challenges: they suffer from particle degeneracy, sample impoverishment, and computational costs arising from resampling.
The goal of this thesis is to:— i) Review the derivation of Kushner-Stratonovich equation from first principles and its extant numerical approximation methods, ii) Study the feedback particle filters as a way of avoiding resampling in particle filters, iii) Study joint state and parameter estimation in time-continuous settings, iv) Apply the notions studied to linear hyperbolic stochastic differential equations.
The interconnection between Itô integrals and stochastic partial differential equations and those of Stratonovich is introduced in anticipation of feedback particle filters. With these ideas and motivated by the variants of ensemble Kalman-Bucy filters founded on the structure of the innovation process, a feedback particle filter with randomly perturbed innovation is proposed. Moreover, feedback particle filters based on coupling of prediction and analysis measures are proposed. They register a better performance than the bootstrap particle filter at lower ensemble sizes.
We study joint state and parameter estimation, both by means of extended state spaces and by use of dual filters. Feedback particle filters seem to perform well in both cases. Finally, we apply joint state and parameter estimation in the advection and wave equation, whose velocity is spatially varying. Two methods are employed: Metropolis Hastings with filter likelihood and a dual filter comprising of Kalman-Bucy filter and ensemble Kalman-Bucy filter. The former performs better than the latter.