Filtern
Volltext vorhanden
- ja (146)
Gehört zur Bibliographie
- ja (146)
Erscheinungsjahr
- 2024 (146) (entfernen)
Dokumenttyp
Sprache
- Englisch (146) (entfernen)
Schlagworte
- Maschinelles Lernen (6)
- Tissue Engineering (6)
- CRISPR/Cas-Methode (3)
- Cognition (3)
- Entzündung (3)
- Immuntherapie (3)
- Induzierte pluripotente Stammzelle (3)
- Kognition (3)
- Nanopartikel (3)
- Simulation (3)
Institut
- Graduate School of Life Sciences (57)
- Theodor-Boveri-Institut für Biowissenschaften (19)
- Institut für Psychologie (10)
- Institut für Organische Chemie (9)
- Neurologische Klinik und Poliklinik (9)
- Institut für Informatik (6)
- Institut für Pharmazie und Lebensmittelchemie (6)
- Rudolf-Virchow-Zentrum (6)
- Deutsches Zentrum für Herzinsuffizienz (DZHI) (5)
- Institut für Mathematik (5)
Sonstige beteiligte Institutionen
- Helmholtz Institute for RNA-based Infection Research (HIRI) (2)
- California Institute of Technology (1)
- Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University in Prague (1)
- Department of Molecular Biology, University Medical Centre Göttingen, Göttingen 37073, Germany (1)
- Deutsches Krebsforschungszentrum Heidelberg (1)
- Deutsches Zentrum für Luft- und Raumfahrt e.V. (1)
- Eberhard Karls Universität Tübingen (1)
- European Space Agency (1)
- Experimental Physics V, University of Wuerzburg (1)
- Fraunhofer Insitut für Silicatforschung ISC (1)
- Fraunhofer-Institute for Silicate Research ISC (1)
- Göttingen Center for Molecular Biosciences, Georg- August University Göttingen, Göttingen 37077, Germany (1)
- Helmholtz Institut für RNA-basierte Infektionsforschung (1)
- Interdisziplinäres Amyloidosezentrum Nordbayern (1)
- LMU München (1)
- Landesbetrieb Landwirtschaft Hessen, Bieneninstitut Kirchhain (1)
- Mathematical Institute, Czech Academy of Sciences (1)
- Michigan State University (1)
- NASA Jet Propulsion Laboratory (1)
- Novartis Pharma AG, Switzerland (1)
- Ostbayerische Technische Hochschule Regensburg (1)
- Research Center of Animal Cognition, Universite Paul Sabatier Toulouse III (1)
- Sahin Lab, F.M. Kirby Neurobiology Center Boston Children’s Hospital, Department of Neurology, Harvard Medical School (1)
- Technische Universität Dresden (1)
- Universität Bielefeld (1)
Among the defense strategies developed in microbes over millions of years, the innate adaptive CRISPR-Cas immune systems have spread across most of bacteria and archaea. The flexibility, simplicity, and specificity of CRISPR-Cas systems have laid the foundation for CRISPR-based genetic tools. Yet, the efficient administration of CRISPR-based tools demands rational designs to maximize the on-target efficiency and off-target specificity. Specifically, the selection of guide RNAs (gRNAs), which play a crucial role in the target recognition of CRISPR-Cas systems, is non-trivial. Despite the fact that the emerging machine learning techniques provide a solution to aid in gRNA design with prediction algorithms, design rules for many CRISPR-Cas systems are ill-defined, hindering their broader applications.
CRISPR interference (CRISPRi), an alternative gene silencing technique using a catalytically dead Cas protein to interfere with transcription, is a leading technique in bacteria for functional interrogation, pathway manipulation, and genome-wide screens. Although the application is promising, it also is hindered by under-investigated design rules. Therefore, in this work, I develop a state-of-art predictive machine learning model for guide silencing efficiency in bacteria leveraging the advantages of feature engineering, data integration, interpretable AI, and automated machine learning. I first systematically investigate the influential factors that attribute to the extent of depletion in multiple CRISPRi genome-wide essentiality screens in Escherichia coli and demonstrate the surprising dominant contribution of gene-specific effects, such as gene expression level. These observations allowed me to segregate the confounding gene-specific effects using a mixed-effect random forest (MERF) model to provide a better estimate of guide efficiency, together with the improvement led by integrating multiple screens. The MERF model outperformed existing tools in an independent high-throughput saturating screen. I next interpret the predictive model to extract the design rules for robust gene silencing, such as the preference for cytosine and disfavoring for guanine and thymine within and around the protospacer adjacent motif (PAM) sequence. I further incorporated the MERF model in a web-based tool that is freely accessible at www.ciao.helmholtz-hiri.de.
When comparing the MERF model with existing tools, the performance of the alternative gRNA design tool optimized for CRISPRi in eukaryotes when applied to bacteria was far from satisfying, questioning the robustness of prediction algorithms across organisms. In addition, the CRISPR-Cas systems exhibit diverse mechanisms albeit with some similarities. The captured predictive patterns from one dataset thereby are at risk of poor generalization when applied across organisms and CRISPR-Cas techniques. To fill the gap, the machine learning approach I present here for CRISPRi could serve as a blueprint for the effective development of prediction algorithms for specific organisms or CRISPR-Cas systems of interest. The explicit workflow includes three principle steps: 1) accommodating the feature set for the CRISPR-Cas system or technique; 2) optimizing a machine learning model using automated machine learning; 3) explaining the model using interpretable AI. To illustrate the applicability of the workflow and diversity of results when applied across different bacteria and CRISPR-Cas systems, I have applied this workflow to analyze three distinct CRISPR-Cas genome-wide screens. From the CRISPR base editor essentiality screen in E. coli, I have determined the PAM preference and sequence context in the editing window for efficient editing, such as A at the 2nd position of PAM, A/TT/TG downstream of PAM, and TC at the 4th to 5th position of gRNAs. From the CRISPR-Cas13a screen in E. coli, in addition to the strong correlation with the guide depletion, the target expression level is the strongest predictor in the model, supporting it as a main determinant of the activation of Cas13-induced immunity and better characterizing the CRISPR-Cas13 system. From the CRISPR-Cas12a screen in Klebsiella pneumoniae, I have extracted the design rules for robust antimicrobial activity across K. pneumoniae strains and provided a predictive algorithm for gRNA design, facilitating CRISPR-Cas12a as an alternative technique to tackle antibiotic resistance.
Overall, this thesis presents an accurate prediction algorithm for CRISPRi guide efficiency in bacteria, providing insights into the determinants of efficient silencing and guide designs. The systematic exploration has led to a robust machine learning approach for effective model development in other bacteria and CRISPR-Cas systems. Applying the approach in the analysis of independent CRISPR-Cas screens not only sheds light on the design rules but also the mechanisms of the CRISPR-Cas systems. Together, I demonstrate that applied machine learning paves the way to a deeper understanding and a broader application of CRISPR-Cas systems.
Cognition refers to the ability to of animals to acquire, process, store and use vital information from the environment. Cognitive processes are necessary to predict the future and reduce the uncertainty of the ever-changing environment. Classically, research on animal cognition focuses on decisive cognitive tests to determine the capacity of a species by the testing the ability of a few individuals. This approach views variability between these tested key individuals as unwanted noise and is thus often neglected. However, inter-individual variability provides important insights to behavioral plasticity, cognitive specialization and brain modularity. Honey bees Apis mellifera are a robust and traditional model for the study of learning, memory and cognition due to their impressive capabilities and rich behavioral repertoire. In this thesis I have applied a novel view on the learning abilities of honey bees by looking explicitly at individual differences in a variety of learning tasks. Are some individual bees consistently smarter than some of her sisters? If so, will a smart individual always perform good independent of the time, the context and the cognitive requirements or do bees show distinct isolated ‘cognitive modules’?
My thesis presents the first comprehensive investigation of consistent individual differences in the cognitive abilities of honey bees. To speak of an individual as behaving consistently, a crucial step is to test the individual multiple times to examine the repeatability of a behavior. I show that free-flying bees remain consistent in a visual discrimination task for three consecutive days. Successively, I explored individual consistency in cognitive proficiency across tasks involving different sensory modalities, contexts and cognitive requirements. I found that free-flying bees show a cognitive specialization between visual and olfactory learning but remained consistent across a simple discrimination task and a complex concept learning task. I wished to further explore individual consistency with respect to tasks of different cognitive complexity, a question that has never been tackled before in an insect. I thus performed a series of four experiments using either visual or olfactory stimuli and a different training context (free-flying and restrained) and tested bees in a discrimination task, reversal learning and negative patterning. Intriguingly, across all these experiments I evidenced the same results: The bees’ performances were consistent across the discrimination task and reversal learning and negative patterning respectively. No association was evidenced between reversal learning and negative patterning. After establishing the existence of consistent individual differences in the cognitive proficiency of honey bees I wished to determine factors which could underlie these differences. Since genetic components are known to underlie inter-individual variability in learning abilities, I studied the effects of genetics on consistency in cognitive proficiency by contrasting bees originating from either from a hive with a single patriline (low genetic diversity) or with multiple patrilines (high genetic diversity). These two groups of bees showed differences in the patterns of individually correlated performances, indicating a genetic component accounts for consistent cognitive individuality. Another major factor underlying variability in learning performances is the individual responsiveness to sucrose solution and to visual stimuli, as evidenced by many studies on restrained bees showing a positive correlation between responsiveness to task relevant stimuli and learning performances. I thus tested whether these relationships between sucrose/visual responsiveness and learning performances are applicable for free-flying bees. Free-flying bees were again subjected to reversal learning and negative patterning and subsequently tested in the laboratory for their responsiveness to sucrose and to light. There was no evidence of a positive relationship between sucrose/visual responsiveness and neither performances of free-flying bees in an elemental discrimination, reversal learning and negative patterning. These findings indicate that relationships established between responsiveness to task relevant stimuli and learning proficiency established in the laboratory with restrained bees might not hold true for a completely different behavioral context i.e. for free-flying bees in their natural environment.
These results show that the honey bee is an excellent insect model to study consistency in cognitive proficiency and to identify the underlying factors. I mainly discuss the results with respect to the question of brain modularity in insects and the adaptive significance of individuality in cognitive abilities for honey bee colonies. I also provide a proposition of research questions which tie in this theme of consistent cognitive proficiency and could provide fruitful areas for future research.
Interpreting gaze behavior is essential in evaluating interaction partners, yet the ‘semantics of gaze’ in dynamic interactions are still poorly understood. We aimed to comprehensively investigate effects of gaze behavior patterns in different conversation contexts, using a two-step, qualitative-quantitative procedure. Participants watched video clips of single persons listening to autobiographic narrations by another (invisible) person. The listener’s gaze behavior was manipulated in terms of gaze direction, frequency and direction of gaze shifts, and blink frequency; emotional context was manipulated through the valence of the narration (neutral/negative). In Experiment 1 (qualitative-exploratory), participants freely described which states and traits they attributed to the listener in each condition, allowing us to identify relevant aspects of person perception and to construct distinct rating scales that were implemented in Experiment 2 (quantitative-confirmatory). Results revealed systematic and differential meanings ascribed to the listener’s gaze behavior. For example, rapid blinking and fast gaze shifts were rated more negatively (e.g., restless and unnatural) than slower gaze behavior; downward gaze was evaluated more favorably (e.g., empathetic) than other gaze aversion types, especially in the emotionally negative context. Overall, our study contributes to a more systematic understanding of flexible gaze semantics in social interaction.
In 2020, cancer was the leading cause of death worldwide, accounting for nearly 10 million deaths. Lung cancer was the most common cancer, with 2.21 million cases per year in both sexes. This non-homogeneous disease is further subdivided into small cell lung cancer (SCLC, 15%) and non-small cell lung cancer (NSCLC, 85%). By 2023, the American Cancer Society estimates that NSCLC will account for 13% of all new cancer cases and 21% of all estimated cancer deaths. In recent years, the treatment of patients with NSCLC has improved with the development of new therapeutic interventions and the advent of targeted and personalised therapies. However, these advances have only marginally improved the five-year survival rate, which remains alarmingly low for patients with NSCLC. This observation highlights the importance of having more appropriate experimental and preclinical models to recapitulate, identify and test novel susceptibilities in NSCLC. In recent years, the Trp53fl/fl KRaslsl-G12D/wt mouse model developed by Tuveson, Jacks and Berns has been the main in vivo model used to study NSCLC. This model mimics ADC and SCC to a certain extent. However, it is limited in its ability to reflect the genetic complexity of NSCLC. In this work, we use CRISPR/Cas9 genome editing with targeted mutagenesis and gene deletions to recapitulate the conditional model. By comparing the Trp53fl/fl KRaslsl- G12D/wt with the CRISPR-mediated Trp53mut KRasG12D, we demonstrated that both showed no differences in histopathological features, morphology, and marker expression. Furthermore, next-generation sequencing revealed a very high similarity in their transcriptional profile. Adeno-associated virus-mediated tumour induction and the modular design of the viral vector allow us to introduce additional mutations in a timely manner. CRISPR-mediated mutation of commonly mutated tumour suppressors in NSCLC reliably recapitulated the phenotypes described in patients in the animal model. Lastly, the dual viral approach could induce the formation of lung tumours not only in constitutive Cas9 expressing animals, but also in wildtype animals. Thus, the implementation of CRISPR genome editing can rapidly advance the repertoire of in vivo models for NSCLC research. Furthermore, it can reduce the necessity of extensive breeding.
Physical regimes characterized by low Mach numbers and steep stratifications pose severe challenges to standard finite volume methods. We present three new methods specifically designed to navigate these challenges by being both low Mach compliant and well-balanced. These properties are crucial for numerical methods to efficiently and accurately compute solutions in the regimes considered.
First, we concentrate on the construction of an approximate Riemann solver within Godunov-type finite volume methods. A new relaxation system gives rise to a two-speed relaxation solver for the Euler equations with gravity. Derived from fundamental mathematical principles, this solver reduces the artificial dissipation in the subsonic regime and preserves hydrostatic equilibria. The solver is particularly stable as it satisfies a discrete entropy inequality, preserves positivity of density and internal energy, and suppresses checkerboard modes.
The second scheme is designed to solve the equations of ideal MHD and combines different approaches. In order to deal with low Mach numbers, it makes use of a low-dissipation version of the HLLD solver and a partially implicit time discretization to relax the CFL time step constraint. A Deviation Well-Balancing method is employed to preserve a priori known magnetohydrostatic equilibria and thereby reduces the magnitude of spatial discretization errors in strongly stratified setups.
The third scheme relies on an IMEX approach based on a splitting of the MHD equations. The slow scale part of the system is discretized by a time-explicit Godunov-type method, whereas the fast scale part is discretized implicitly by central finite differences. Numerical dissipation terms and CFL time step restriction of the method depend solely on the slow waves of the explicit part, making the method particularly suited for subsonic regimes. Deviation Well-Balancing ensures the preservation of a priori known magnetohydrostatic equilibria.
The three schemes are applied to various numerical experiments for the compressible Euler and ideal MHD equations, demonstrating their ability to accurately simulate flows in regimes with low Mach numbers and strong stratification even on coarse grids.
The WHO-designated neglected-disease pathogen Chlamydia trachomatis (CT) is a gram-negative bacterium responsible for the most frequently diagnosed sexually transmitted infection worldwide. CT infections can lead to infertility, blindness and reactive arthritis, among others. CT acts as an infectious agent by its ability to evade the immune response of its host, which includes the impairment of the NF-κB mediated inflammatory response and the Mcl1 pro-apoptotic pathway through its deubiquitylating, deneddylating and transacetylating enzyme ChlaDUB1 (Cdu1). Expression of Cdu1 is also connected to host cell Golgi apparatus fragmentation, a key process in CT infections.
Cdu1 may this be an attractive drug target for the treatment of CT infections. However, a lead molecule for the development of novel potent inhibitors has been unknown so far. Sequence alignments and phylogenetic searches allocate Cdu1 in the CE clan of cysteine proteases. The adenovirus protease (adenain) also belongs to this clan and shares a high degree of structural similarity with Cdu1. Taking advantage of topological similarities between the active sites of Cdu1 and adenain, a target-hopping approach on a focused set of adenain inhibitors, developed at Novartis, has been pursued. The thereby identified cyano-pyrimidines represent the first active-site directed covalent reversible inhibitors for Cdu1. High-resolution crystal structures of Cdu1 in complex with the covalently bound cyano-pyrimidines as well as with its substrate ubiquitin have been elucidated. The structural data of this thesis, combined with enzymatic assays and covalent docking studies, provide valuable insights into Cdu1s activity, substrate recognition, active site pocket flexibility and potential hotspots for ligand interaction. Structure-informed drug design permitted the optimization of this cyano-pyrimidine based scaffold towards HJR108, the first molecule of its kind specifically designed to disrupt the function of Cdu1. The structures of potentially more potent and selective Cdu1 inhibitors are herein proposed.
This thesis provides important insights towards our understanding of the structural basis of ubiquitin recognition by Cdu1, and the basis to design highly specific Cdu1 covalent inhibitors.
This dissertation explores the development and assessment of inhibitory control – a crucial component of executive functions – in young children. Inhibitory control, defined as the ability to suppress inappropriate responses (Verbruggen & Logan, 2008), is essential for adaptable and goal-oriented behavior. The rapid and non-linear development of this cognitive function in early childhood presents unique challenges for accurate assessment. As children age, they often exhibit a ceiling effect in terms of response accuracy (Petersen et al., 2016), underscoring the need to consider response latency as well. Ideally, combining response latency with accuracy could yield a more precise measure of inhibitory control (e.g., Magnus et al., 2019), facilitating a detailed tracking of developmental changes in inhibitory control across a wider age spectrum. The three studies of this dissertation collectively aim to clarify the relationship between response accuracy, response latency, and inhibitory control across different stages of child development. Each study utilizes a computerized Pointing Stroop Task (Berger et al., 2000) to measure inhibitory control, examining the task's validity and the integration of dual metrics for a more comprehensive evaluation.
The first study focuses on establishing the validity of using both response accuracy and latency as indicators of inhibitory control. Utilizing the framework of explanatory item-response modeling (De Boeck & Wilson, 2004), the study revealed how the task characteristics congruency and item position influence both the difficulty level and timing aspects in young children’s responses in the computerized Pointing Stroop task. Further, this study found that integrating response accuracy with latency, even in a basic manner, provides additional insights. Building upon these findings, the second study investigates the nuances of integrating response accuracy and latency, examining whether this approach can account for age-related differences in inhibitory control. It also explores whether response latencies may contain different information depending on the age and proficiency of the children. The study leverages novel and established methodological perspectives to integrate response accuracy and latency into a single metric, showing the potential applicability of different approaches for assessing inhibitory control development. The third study extends the investigation to a longitudinal perspective, exploring the dynamic relationship between response accuracy, latency, and inhibitory control over time. It assesses whether children who achieve high accuracy at an earlier age show faster improvement in response latency, suggesting a non-linear maturation pathway of inhibitory control. The study also examines if the predictive value of early response latency for later fluid intelligence is dependent on the response accuracy level.
Together, these empirical studies contribute to a more robust understanding of the complex interaction between inhibitory control, response accuracy, and response latency, facilitating valid evaluations of cognitive capabilities in children. Moreover, the findings may have practical implications for designing educational strategies and clinical interventions that address the developmental trajectory of inhibitory control. The nuanced approach advocated in this dissertation suggests prioritizing accuracy in assessment and interventions during the early stages of children's cognitive development, gradually shifting the focus to response latency as children mature and secure their inhibitory control abilities.
The focus of this thesis is on analysing a linear stochastic partial differential equation (SPDE) with a bounded domain. The first part of the thesis commences with an examination of a one-dimensional SPDE. In this context, we construct estimators for the parameters of a parabolic SPDE based on discrete observations of a solution in time and space on a bounded domain. We establish central limit theorems for a high-frequency asymptotic regime, showing substantially smaller asymptotic variances compared to existing estimation methods. Moreover, asymptotic confidence intervals are directly feasible. Our approach builds upon realized volatilities and their asymptotic illustration as the response of a log-linear model with a spatial explanatory variable. This yields efficient estimators based on realized volatilities with optimal rates of convergence and minimal variances. We demonstrate our results by Monte Carlo simulations.
Extending this framework, we analyse a second-order SPDE model in multiple space dimensions in the second part of this thesis and develop estimators for the parameters of this model based on discrete observations in time and space on a bounded domain. While parameter estimation for one and two spatial dimensions was established in recent literature, this is the first work that generalizes the theory to a general, multi-dimensional framework. Our methodology enables the construction of an oracle estimator for volatility within the underlying model. For proving central limit theorems, we use a high-frequency observation scheme. To showcase our results, we conduct a Monte Carlo simulation, highlighting the advantages of our novel approach in a multi-dimensional context.
Two-dimensional lattices are in the focus of research in modern solid state physics due to their novel and exotic electronic properties with tremendous potential for seminal future applications. Of particular interest within this research field are quantum spin Hall insulators which are characterized by an insulating bulk with symmetry-protected metallic edge states. For electrons within these one-dimensional conducting channels, spin-momentum locking enables dissipationless transport - a property which promises nothing short of a revolution for electronic devices. So far, however, quantum spin Hall materials require enormous efforts to be realized such as cryogenic temperatures or ultra-high vacuum. A potential candidate to overcome these shortcomings are two-dimensional lattices of the topological semi-metal antimony due to their potential to host the quantum spin Hall effect while offering improved resilience against oxidation.
In this work, two-dimensional lattices of antimony on different substrates, namely Ag(111), InSb(111) and SiC(0001), are investigated regarding their atomic structure and electronic properties with complimentary surface sensitive techniques. In addition, a systematic oxidation study compares the stability of Sb-SiC(0001) with that of the two-dimensional topological insulators bismuthene-SiC(0001) and indenene-SiC(0001).
A comprehensive experimental analysis of the \((\sqrt{3}\times\sqrt{3})R30^\circ\) Sb-Ag(111) surface, including X-ray standing wave measurements, disproves the proclaimed formation of a buckled antimonene lattice in literature. The surface lattice can instead be identified as a metallic Ag\(_2\)Sb surface alloy.
Antimony on InSb(111) shows an unstrained Volmer-Weber island growth due to its large lattice mismatch to the substrate. The concomitant moir\'{e} situation at the interface imprints mainly in a periodic height corrugation of the antimony islands which as observed with scanning tunneling microscopy. On islands with various thicknesses, quasiparticle interference patterns allow to trace the topological surface state of antimony down to the few-layer limit.
On SiC(0001), two different two-dimensional antimony surface reconstructions are identified. Firstly, a metallic triangular $1\times1$ lattice which constitutes the antimony analogue to the topological insulator indenene. Secondly, an insulating asymmetric kagome lattice which represents the very first realized atomic surface kagome lattice.
A comparative, systematic oxidation study of elemental (sub-)monolayer materials on SiC(0001) reveals a high sensitivity of indenene and bismuthene to small dosages of oxygen. An improved resilience is found for Sb-SiC(0001) which, however, oxidizes nevertheless if exposed to oxygen. These surface lattices are therefore not suitable for future applications without additional protective measures.
In this thesis, a variety of Fokker--Planck (FP) optimal control problems are investigated. Main emphasis is put on a first-- and second--order analysis of different optimal control problems, characterizing optimal controls, establishing regularity results for optimal controls, and providing a numerical analysis for a Galerkin--based numerical scheme.
The Fokker--Planck equation is a partial differential equation (PDE) of linear parabolic type deeply connected to the theory of stochastic processes and stochastic differential equations. In essence, it describes the evolution over time of the probability distribution of the state of an object or system of objects under the influence of both deterministic and stochastic forces.
The FP equation is a cornerstone in understanding and modeling phenomena ranging from the diffusion and motion of molecules in a fluid to the fluctuations in financial markets.
Two different types of optimal control problems are analyzed in this thesis. On the one hand, Fokker--Planck ensemble optimal control problems are considered that have a wide range of applications in controlling a system of multiple non--interacting objects. In this framework, the goal is to collectively drive each object into a desired state.
On the other hand, tracking--type control problems are investigated, commonly used in parameter identification problems or stemming from the field of inverse problems.
In this framework, the aim is to determine certain parameters or functions of the FP equation, such that the resulting probability distribution function takes a desired form, possibly observed by measurements.
In both cases, we consider FP models where the control functions are part of the drift, arising only from the deterministic forces of the system. Therefore, the FP optimal control problem has a bilinear control structure.
Box constraints on the controls may be present, and the focus is on time--space dependent controls for ensemble--type problems and on only time--dependent controls for tracking--type optimal control problems.
In the first chapter of the thesis, a proof of the connection between the FP equation and stochastic differential equations is provided. Additionally, stochastic optimal control problems, aiming to minimize an expected cost value, are introduced, and the corresponding formulation within a deterministic FP control framework is established.
For the analysis of this PDE--constrained optimal control problem, the existence, and regularity of solutions to the FP problem are investigated. New $L^\infty$--estimates for solutions are established for low space dimensions under mild assumptions on the drift. Furthermore, based on the theory of Bessel potential spaces, new smoothness properties are derived for solutions to the FP problem in the case of only time--dependent controls. Due to these properties, the control--to--state map, which associates the control functions with the corresponding solution of the FP problem, is well--defined, Fréchet differentiable and compact for suitable Lebesgue spaces or Sobolev spaces.
The existence of optimal controls is proven under various assumptions on the space of admissible controls and objective functionals. First--order optimality conditions are derived using the adjoint system. The resulting characterization of optimal controls is exploited to achieve higher regularity of optimal controls, as well as their state and co--state functions.
Since the FP optimal control problem is non--convex due to its bilinear structure, a first--order analysis should be complemented by a second--order analysis.
Therefore, a second--order analysis for the ensemble--type control problem in the case of $H^1$--controls in time and space is performed, and sufficient second--order conditions are provided. Analogous results are obtained for the tracking--type problem for only time--dependent controls.
The developed theory on the control problem and the first-- and second--order optimality conditions is applied to perform a numerical analysis for a Galerkin discretization of the FP optimal control problem. The main focus is on tracking-type problems with only time--dependent controls. The idea of the presented Galerkin scheme is to first approximate the PDE--constrained optimization problem by a system of ODE--constrained optimization problems. Then, conditions on the problem are presented such that the convergence of optimal controls from one problem to the other can be guaranteed.
For this purpose, a class of bilinear ODE--constrained optimal control problems arising from the Galerkin discretization of the FP problem is analyzed. First-- and second--order optimality conditions are established, and a numerical analysis is performed. A discretization with linear finite elements for the state and co--state problem is investigated, while the control functions are approximated by piecewise constant or piecewise quadratic continuous polynomials. The latter choice is motivated by the bilinear structure of the optimal control problem, allowing to overcome the discrepancies between a discretize--then--optimize and optimize--then--discretize approach. Moreover, second--order accuracy results are shown using the space of continuous, piecewise quadratic polynomials as the discrete space of controls. Lastly, the theoretical results and the second--order convergence rates are numerically verified.