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One third of the world's population lives in areas where earthquakes causing at least slight damage are frequently expected. Thus, the development and testing of global seismicity models is essential to improving seismic hazard estimates and earthquake-preparedness protocols for effective disaster-risk mitigation. Currently, the availability and quality of geodetic data along plate-boundary regions provides the opportunity to construct global models of plate motion and strain rate, which can be translated into global maps of forecasted seismicity. Moreover, the broad coverage of existing earthquake catalogs facilitates in present-day the calibration and testing of global seismicity models. As a result, modern global seismicity models can integrate two independent factors necessary for physics-based, long-term earthquake forecasting, namely interseismic crustal strain accumulation and sudden lithospheric stress release.
In this dissertation, I present the construction of and testing results for two global ensemble seismicity models, aimed at providing mean rates of shallow (0-70 km) earthquake activity for seismic hazard assessment. These models depend on the Subduction Megathrust Earthquake Rate Forecast (SMERF2), a stationary seismicity approach for subduction zones, based on the conservation of moment principle and the use of regional "geodesy-to-seismicity" parameters, such as corner magnitudes, seismogenic thicknesses and subduction dip angles. Specifically, this interface-earthquake model combines geodetic strain rates with instrumentally-recorded seismicity to compute long-term rates of seismic and geodetic moment. Based on this, I derive analytical solutions for seismic coupling and earthquake activity, which provide this earthquake model with the initial abilities to properly forecast interface seismicity. Then, I integrate SMERF2 interface-seismicity estimates with earthquake computations in non-subduction zones provided by the Seismic Hazard Inferred From Tectonics based on the second iteration of the Global Strain Rate Map seismicity approach to construct the global Tectonic Earthquake Activity Model (TEAM). Thus, TEAM is designed to reduce number, and potentially spatial, earthquake inconsistencies of its predecessor tectonic earthquake model during the 2015-2017 period. Also, I combine this new geodetic-based earthquake approach with a global smoothed-seismicity model to create the World Hybrid Earthquake Estimates based on Likelihood scores (WHEEL) model. This updated hybrid model serves as an alternative earthquake-rate approach to the Global Earthquake Activity Rate model for forecasting long-term rates of shallow seismicity everywhere on Earth.
Global seismicity models provide scientific hypotheses about when and where earthquakes may occur, and how big they might be. Nonetheless, the veracity of these hypotheses can only be either confirmed or rejected after prospective forecast evaluation. Therefore, I finally test the consistency and relative performance of these global seismicity models with independent observations recorded during the 2014-2019 pseudo-prospective evaluation period. As a result, hybrid earthquake models based on both geodesy and seismicity are the most informative seismicity models during the testing time frame, as they obtain higher information scores than their constituent model components. These results support the combination of interseismic strain measurements with earthquake-catalog data for improved seismicity modeling. However, further prospective evaluations are required to more accurately describe the capacities of these global ensemble seismicity models to forecast longer-term earthquake activity.
The sea level rise induced intensification of coastal floods is a serious threat to many regions in proximity to the ocean. Although severe flood events are rare they can entail enormous damage costs, especially when built-up areas are inundated. Fortunately, the mean sea level advances slowly and there is enough time for society to adapt to the changing environment. Most commonly, this is achieved by the construction or reinforcement of flood defence measures such as dykes or sea walls but also land use and disaster management are widely discussed options. Overall, albeit the projection of sea level rise impacts and the elaboration of adequate response strategies is amongst the most prominent topics in climate impact research, global damage estimates are vague and mostly rely on the same assessment models. The thesis at hand contributes to this issue by presenting a distinctive approach which facilitates large scale assessments as well as the comparability of results across regions. Moreover, we aim to improve the general understanding of the interplay between mean sea level rise, adaptation, and coastal flood damage.
Our undertaking is based on two basic building blocks. Firstly, we make use of macroscopic flood-damage functions, i.e. damage functions that provide the total monetary damage within a delineated region (e.g. a city) caused by a flood of certain magnitude. After introducing a systematic methodology for the automatised derivation of such functions, we apply it to a total of 140 European cities and obtain a large set of damage curves utilisable for individual as well as comparative damage assessments. By scrutinising the resulting curves, we are further able to characterise the slope of the damage functions by means of a functional model. The proposed function has in general a sigmoidal shape but exhibits a power law increase for the relevant range of flood levels and we detect an average exponent of 3.4 for the considered cities. This finding represents an essential input for subsequent elaborations on the general interrelations of involved quantities.
The second basic element of this work is extreme value theory which is employed to characterise the occurrence of flood events and in conjunction with a damage function provides the probability distribution of the annual damage in the area under study. The resulting approach is highly flexible as it assumes non-stationarity in all relevant parameters and can be easily applied to arbitrary regions, sea level, and adaptation scenarios. For instance, we find a doubling of expected flood damage in the city of Copenhagen for a rise in mean sea levels of only 11 cm. By following more general considerations, we succeed in deducing surprisingly simple functional expressions to describe the damage behaviour in a given region for varying mean sea levels, changing storm intensities, and supposed protection levels. We are thus able to project future flood damage by means of a reduced set of parameters, namely the aforementioned damage function exponent and the extreme value parameters. Similar examinations are carried out to quantify the aleatory uncertainty involved in these projections. In this regard, a decrease of (relative) uncertainty with rising mean sea levels is detected. Beyond that, we demonstrate how potential adaptation measures can be assessed in terms of a Cost-Benefit Analysis. This is exemplified by the Danish case study of Kalundborg, where amortisation times for a planned investment are estimated for several sea level scenarios and discount rates.
Solar-like stars maintain their magnetic fields thanks to a dynamo mechanism. The Babcock-Leighton dynamo is one possible dynamo that has the particularity to require magnetic flux tubes. Magnetic flux tubes are assumed to form at the bottom of the convective zone and rise buoyantly to the surface. A delayed dynamo model has been suggested, where the delay accounts for the rise time of the magnetic flux tubes; a time, that has been ignored by former studies.
The present thesis aims to study the applicability of the flux tube/Babcock-Leighton dynamo to other stars. To do so, we attempt to constrain the rise time of magnetic flux tubes thanks to the first fully compressible MHD simulations of rising magnetic flux tubes in stratified rotating spherical shells.
Such simulations are limited to an unrealistic parameter space, therefore, a scaling relation is required to scale the results to realistic physical regimes. We extended earlier works on 2D scaling relations and derived a general scaling law valid for both 2D and 3D. We then carried out two large series of numerical experiments and verified that the scaling law we have derived indeed applies to the fully non-linear case. It allowed us to extract a constraint for the rise time of magnetic flux tubes that is valid for any solar-like star. We finally introduced this constraint to a delayed dynamo model.
By carrying out simulations of a mean-field, delayed, flux tube/Babcock-Leighton dynamo, we were able to identify a new dynamo regime resulting from the delay. This regime requires delays about an entire cycle and exhibits subequipartition magnetic activity. Revealing this new regime shows that even for long delays the flux tube/Babcock-Leighton dynamo can still deliver non-decaying solutions and remains a good candidate for a wide range of solar-like stars.
Monoclonal antibodies (mAbs) are an innovative group of drugs with increasing clinical importance in oncology, combining high specificity with generally low toxicity. There are, however, numerous challenges associated with the development of mAbs as therapeutics. Mechanistic understanding of factors that govern the pharmacokinetics (PK) of mAbs is critical for drug development and the optimisation of effective therapies; in particular, adequate dosing strategies can improve patient quality life and lower drug cost. Physiologically-based PK (PBPK) models offer a physiological and mechanistic framework, which is of advantage in the context of animal to human extrapolation. Unlike for small molecule drugs, however, there is no consensus on how to model mAb disposition in a PBPK context. Current PBPK models for mAb PK hugely vary in their representation of physiology and parameterisation. Their complexity poses a challenge for their applications, e.g., translating knowledge from animal species to humans.
In this thesis, we developed and validated a consensus PBPK model for mAb disposition taking into account recent insights into mAb distribution (antibody biodistribution coefficients and interstitial immunoglobulin G (IgG) pharmacokinetics) to predict tissue PK across several pre-clinical species and humans based on plasma data only. The model allows to a priori predict target-independent (unspecific) mAb disposition processes as well as mAb disposition in concentration ranges, for which the unspecific clearance (CL) dominates target-mediated CL processes. This is often the case for mAb therapies at steady state dosing.
The consensus PBPK model was then used and refined to address two important problems:
1) Immunodeficient mice are crucial models to evaluate mAb efficacy in cancer therapy. Protection from elimination by binding to the neonatal Fc receptor is known to be a major pathway influencing the unspecific CL of both, endogenous and therapeutic IgG. The concentration of endogenous IgG, however, is reduced in immunodeficient mouse models, and this effect on unspecific mAb CL is unknown, yet of great importance for the extrapolation to human in the context of mAb cancer therapy.
2) The distribution of mAbs into solid tumours is of great interest. To comprehensively investigate mAb distribution within tumour tissue and its implications for therapeutic efficacy, we extended the consensus PBPK model by a detailed tumour distribution model incorporating a cell-level model for mAb-target interaction. We studied the impact of variations in tumour microenvironment on therapeutic efficacy and explored the plausibility of different mechanisms of action in mAb cancer therapy.
The mathematical findings and observed phenomena shed new light on therapeutic utility and dosing regimens in mAb cancer treatment.
Continuous insight into biological processes has led to the development of large-scale, mechanistic systems biology models of pharmacologically relevant networks. While these models are typically designed to study the impact of diverse stimuli or perturbations on multiple system variables, the focus in pharmacological research is often on a specific input, e.g., the dose of a drug, and a specific output related to the drug effect or response in terms of some surrogate marker.
To study a chosen input-output pair, the complexity of the interactions as well as the size of the models hinders easy access and understanding of the details of the input-output relationship.
The objective of this thesis is the development of a mathematical approach, in specific a model reduction technique, that allows (i) to quantify the importance of the different state variables for a given input-output relationship, and (ii) to reduce the dynamics to its essential features -- allowing for a physiological interpretation of state variables as well as parameter estimation in the statistical analysis of clinical data. We develop a model reduction technique using a control theoretic setting by first defining a novel type of time-limited controllability and observability gramians for nonlinear systems. We then show the superiority of the time-limited generalised gramians for nonlinear systems in the context of balanced truncation for a benchmark system from control theory.
The concept of time-limited controllability and observability gramians is subsequently used to introduce a state and time-dependent quantity called the input-response (ir) index that quantifies the importance of state variables for a given input-response relationship at a particular time.
We subsequently link our approach to sensitivity analysis, thus, enabling for the first time the use of sensitivity coefficients for state space reduction. The sensitivity based ir-indices are given as a product of two sensitivity coefficients. This allows not only for a computational more efficient calculation but also for a clear distinction of the extent to which the input impacts a state variable and the extent to which a state variable impacts the output.
The ir-indices give insight into the coordinated action of specific state variables for a chosen input-response relationship.
Our developed model reduction technique results in reduced models that still allow for a mechanistic interpretation in terms of the quantities/state variables of the original system, which is a key requirement in the field of systems pharmacology and systems biology and distinguished the reduced models from so-called empirical drug effect models. The ir-indices are explicitly defined with respect to a reference trajectory and thereby dependent on the initial state (this is an important feature of the measure). This is demonstrated for an example from the field of systems pharmacology, showing that the reduced models are very informative in their ability to detect (genetic) deficiencies in certain physiological entities. Comparing our novel model reduction technique to the already existing techniques shows its superiority.
The novel input-response index as a measure of the importance of state variables provides a powerful tool for understanding the complex dynamics of large-scale systems in the context of a specific drug-response relationship. Furthermore, the indices provide a means for a very efficient model order reduction and, thus, an important step towards translating insight from biological processes incorporated in detailed systems pharmacology models into the population analysis of clinical data.
While patients are known to respond differently to drug therapies, current clinical practice often still follows a standardized dosage regimen for all patients. For drugs with a narrow range of both effective and safe concentrations, this approach may lead to a high incidence of adverse events or subtherapeutic dosing in the presence of high patient variability. Model-informedprecision dosing (MIPD) is a quantitative approach towards dose individualization based on mathematical modeling of dose-response relationships integrating therapeutic drug/biomarker monitoring (TDM) data. MIPD may considerably improve the efficacy and safety of many drug therapies. Current MIPD approaches, however, rely either on pre-calculated dosing tables or on simple point predictions of the therapy outcome. These
approaches lack a quantification of uncertainties and the ability to account for effects that are delayed. In addition, the underlying models are not improved while applied to patient data. Therefore, current approaches are not well suited for informed clinical decision-making based on a differentiated understanding of the individually predicted therapy outcome.
The objective of this thesis is to develop mathematical approaches for MIPD, which (i) provide efficient fully Bayesian forecasting of the individual therapy outcome including associated uncertainties, (ii) integrate Markov decision processes via reinforcement learning (RL) for a comprehensive decision framework for dose individualization, (iii) allow for continuous learning across patients and hospitals. Cytotoxic anticancer chemotherapy with its major dose-limiting toxicity, neutropenia, serves as a therapeutically relevant application example.
For more comprehensive therapy forecasting, we apply Bayesian data assimilation (DA) approaches, integrating patient-specific TDM data into mathematical models of chemotherapy-induced neutropenia that build on prior population analyses. The value of uncertainty quantification is demonstrated as it allows reliable computation of the patient-specific probabilities of relevant clinical quantities, e.g., the neutropenia grade. In view of novel home monitoring devices that increase the amount of TDM data available, the data processing of
sequential DA methods proves to be more efficient and facilitates handling of the variability between dosing events.
By transferring concepts from DA and RL we develop novel approaches for MIPD. While DA-guided dosing integrates individualized uncertainties into dose selection, RL-guided dosing provides a framework to consider delayed effects of dose selections. The combined
DA-RL approach takes into account both aspects simultaneously and thus represents a holistic approach towards MIPD. Additionally, we show that RL can be used to gain insights into important patient characteristics for dose selection. The novel dosing strategies substantially reduce the occurrence of both subtherapeutic and life-threatening neutropenia grades in a simulation study based on a recent clinical study (CEPAC-TDM trial) compared to currently used MIPD approaches.
If MIPD is to be implemented in routine clinical practice, a certain model bias with respect to the underlying model is inevitable, as the models are typically based on data from comparably small clinical trials that reflect only to a limited extent the diversity in real-world patient populations. We propose a sequential hierarchical Bayesian inference framework that enables continuous cross-patient learning to learn the underlying model parameters of the target patient population. It is important to note that the approach only requires summary information of the individual patient data to update the model. This separation of the individual inference from population inference enables implementation across different centers of care.
The proposed approaches substantially improve current MIPD approaches, taking into account new trends in health care and aspects of practical applicability. They enable progress towards more informed clinical decision-making, ultimately increasing patient benefits beyond the current practice.
Point processes are a common methodology to model sets of events. From earthquakes to social media posts, from the arrival times of neuronal spikes to the timing of crimes, from stock prices to disease spreading -- these phenomena can be reduced to the occurrences of events concentrated in points. Often, these events happen one after the other defining a time--series.
Models of point processes can be used to deepen our understanding of such events and for classification and prediction. Such models include an underlying random process that generates the events. This work uses Bayesian methodology to infer the underlying generative process from observed data. Our contribution is twofold -- we develop new models and new inference methods for these processes.
We propose a model that extends the family of point processes where the occurrence of an event depends on the previous events. This family is known as Hawkes processes. Whereas in most existing models of such processes, past events are assumed to have only an excitatory effect on future events, we focus on the newly developed nonlinear Hawkes process, where past events could have excitatory and inhibitory effects. After defining the model, we present its inference method and apply it to data from different fields, among others, to neuronal activity.
The second model described in the thesis concerns a specific instance of point processes --- the decision process underlying human gaze control. This process results in a series of fixated locations in an image. We developed a new model to describe this process, motivated by the known Exploration--Exploitation dilemma. Alongside the model, we present a Bayesian inference algorithm to infer the model parameters.
Remaining in the realm of human scene viewing, we identify the lack of best practices for Bayesian inference in this field. We survey four popular algorithms and compare their performances for parameter inference in two scan path models.
The novel models and inference algorithms presented in this dissertation enrich the understanding of point process data and allow us to uncover meaningful insights.
My thesis focused on the predictions of the activation-based model of Lewis and Vasishth (2005) to investigate the evidence for the use of the memory system in the formation of non-local dependencies in sentence comprehension.
The activation-based model, which follows the Adaptive Control of Thought-Rational framework (ACT-R; Anderson et al., 2004), has been used to explain locality effects and similarity-based interference by assuming that dependencies are resolved by a cue-based retrieval mechanism, and that the retrieval mechanism is affected by decay and interference.
Both locality effects and (inhibitory) similarity-based interference cause increased difficulty (e.g., longer reading times) at the site of the dependency completion where a retrieval is assumed: (I) Locality effects are attributed to the increased difficulty in the retrieval of a dependent when the distance from its retrieval site is increased. (II) Similarity-based interference is attributed to the retrieval being affected by the presence of items which have similar features as the dependent that needs to be retrieved.
In this dissertation, I investigated some findings problematic to the activation-based model, namely, facilitation where locality effects are expected (e.g., Levy, 2008), and the lack of similarity-based interference from the number feature in grammatical sentences (e.g., Wagers et al., 2009). In addition, I used individual differences in working memory capacity and reading fluency as a way to validate the theories investigated (Underwood, 1975), and computational modeling to achieve a more precise account of the phenomena.
Regarding locality effects, by using self-paced reading and eye-tracking-while reading methods with Spanish and German data, this dissertation yielded two main findings: (I) Locality effects seem to be modulated by working memory capacity, with high-capacity participants showing expectation-driven facilitation. (II) Once expectations and other potential confounds are controlled using baselines, with increased distance, high-capacity readers can show a slow-down (i.e., locality effects) and low-capacity readers can show a speedup. While the locality effects are compatible with the activation-based model, simulations show that the speedup of low-capacity readers can only be accounted for by changing some of the assumptions of the activation-based model.
Regarding similarity-based interference, two relatively high-powered self-paced reading experiments in German using grammatical sentences yielded a slowdown at the verb as predicted by the activation-based model. This provides evidence in favor of dependency creation via cue-based retrieval, and in contrast with the view that cue-based retrieval is a reanalysis mechanism (Wagers et al., 2009).
Finally, the same experimental results that showed inhibitory interference from the number feature are used for a finer grain evaluation of the retrieval process. Besides Lewis and Vasishth’s (2005) activation-based model, also McElree’s (2000) direct-access model can account for inhibitory interference. These two models assume a cue-based retrieval mechanism to build dependencies, but they are based on different assumptions. I present a computational evaluation of the predictions of these two theories of retrieval. The models were compared by implementing them in a Bayesian hierarchical framework. The evaluation of the models reveals that some aspects of the data fit better under the direct access model than under the activation-based model. However, a simple extension of the activation-based model provides a comparable fit to the direct access model. This serves as a proof of concept showing potential ways to improve the original activation-based model.
In conclusion, this thesis adds to the body of evidence that argues for the use of the general memory system in dependency resolution, and in particular for a cue-based retrieval mechanism. However, it also shows that some of the default assumptions inherited from ACT-R in the activation-based model need to be revised.
Lie group method in combination with Magnus expansion is utilized to develop a universal method applicable to solving a Sturm–Liouville Problem (SLP) of any order with arbitrary boundary conditions. It is shown that the method has ability to solve direct regular and some singular SLPs of even orders (tested up to order eight), with a mix of boundary conditions (including non-separable and finite singular endpoints), accurately and efficiently.
The present technique is successfully applied to overcome the difficulties in finding suitable sets of eigenvalues so that the inverse SLP problem can be effectively solved.
Next, a concrete implementation to the inverse Sturm–Liouville problem
algorithm proposed by Barcilon (1974) is provided. Furthermore, computational feasibility and applicability of this algorithm to solve inverse Sturm–Liouville problems of order n=2,4 is verified successfully. It is observed that the method is successful even in the presence of significant noise, provided that the assumptions of the algorithm are satisfied.
In conclusion, this work provides methods that can be adapted successfully for solving a direct (regular/singular) or inverse SLP of an arbitrary order with arbitrary boundary conditions.