Recent developments in single-cell measurement technologies have yielded dramatic increases in throughput (measured cells per experiment) and dimensionality (measured features per cell). In particular, the introduction of mass cytometry has made possible the simultaneous quantification of dozens of protein species in millions of individual cells in a single experiment. The raw data produced by such high-dimensional single-cell measurements provide unprecedented potential to reveal the phenotypic heterogeneity of cellular systems. In order to realize this potential, novel computational techniques are required to extract knowledge from these complex data. Analysis of single-cell data is a new challenge for computational biology, as early development in the field was tailored to technologies that sacrifice single-cell resolution, such as DNA microarrays. The challenges for single-cell data are quite distinct and require multidimensional modeling of complex population structure. Particular challenges include nonlinear relationships between measured features and non-convex subpopulations. This thesis integrates methods from computational geometry and network analysis to develop a framework for identifying the population structure in high-dimensional single-cell data. At the center of this framework is PhenoGraph, and algorithmic approach to defining subpopulations, which when applied to healthy bone marrow data was shown to reconstruct known immune cell types automatically without prior information. PhenoGraph demonstrated superior accuracy, robustness, and efficiency, compared to other methods. The data-driven approach becomes truly powerful when applied to less characterized systems, such as malignancies, in which the tissue diverges from its healthy population composition. Applying PhenoGraph to bone marrow samples from a cohort of acute myeloid leukemia (AML) patients, the thesis presents several insights into the pathophysiology of AML, which were extracted by virtue of the computational isolation of leukemic subpopulations. For example, it is shown that leukemic subpopulations diverge from healthy bone marrow but not without bound: Leukemic cells are apparently free to explore only a restricted phenotypic space that mimics normal myeloid development. Further, the phenotypic composition of a sample is associated with its cytogenetics, demonstrating a genetic influence on the population structure of leukemic bone marrow. The thesis goes on to show that functional heterogeneity of leukemic samples can be computationally inferred from molecular perturbation data. Using a variety of methods that build on PhenoGraph's foundations, the thesis presents a characterization of leukemic subpopulations based on an inferred stem-like signaling pattern. Through this analysis, it is shown that surface phenotypes often fail to reflect the true underlying functional state of the subpopulation, and that this functional stem-like state is in fact a powerful predictor of survival in large, independent cohorts. Altogether, the thesis takes the existence and importance of cellular heterogeneity as its starting point and presents a mathematical framework and computational toolkit for analyzing samples from this perspective. It is shown that phenotypic and functional heterogeneity are robust characteristics of acute myeloid leukemia with clinically significant ramifications.

Photovoltaic energy is the most promising future energy source. Therefore, strong efforts are made to improve their price-to-efficiency ratio. New technologies and materials are being involved in the production, such as poly-crystalline materials rather than mono-crystalline silicon. Some of these materials are based on copperchalcopyrite with advantageous properties like directly tunable band gap, high absorption coefficients, low deposition temperatures, low-cost materials and capability of deposition on suitable materials. However, correlation between the thin film materials characteristics and device performance are not well understood, and increasing the efficiency needs an exhaustive comprehension of the different phenomena involved in their performance, such as role of defects, doping concentrations and potentials, which requires the development of innovative techniques for the characterization. Electron holography in the TEM would be very helpful, because it allows the quantitative reconstruction of the complex object wave. The measurement of phase and amplitude of the wave makes it possible to determine the potential in the object studied. In this manner, electron holography is a powerful tool for materials characterization at nanometre scale because it relates potential distributions with structure. However, artefacts can be introduced in the measurement. Therefore, the procedure of acquisition, reconstruction and correction of artefacts of the electron holograms, fundamental for the interpretation of the results in terms of potential, are in detail presented. Moreover, the object of study exhibits challenges to the technique because of their polycrystalline structure, which introduces dynamic interaction with the electron beam sometimes stronger than the desired one. Consequently it is necessary to have an adequate measurement procedure. To overcome this limitation, a characterization method including in-situ stimuli is proposed and applied to crystalline silicon and CIGS solar cells. For this, a suitable sample preparation procedure with Focused Ion Beam (FIB) milling, and a specially designed sample holder allowing illumination with light and biasing a TEM sample are developed and applied to solar cells. As result of the work, it is shown that expectedly the electron illumination has an important influence. It produces larger generation rates than 1 sun standard illumination. As counterpart, the recombination processes occurring at the surface of the small and thin sample tend to reduce the potential generated by the illumination. As consequence, only the p-n junction potential is usually measured. To produce an appreciable effect by illumination with light, the TEM lamella must be thicker, and the illumination intensity of the light must be strongly increased. This thesis realises the first extensive study of the application of electron holography to the measurement of potentials in solar cells applying in-situ illumination and biasing. The experimental findings were corroborated by simulation calculations. They show that the processes in the objects are essentially correctly understood, however, quantitative interpretation is not yet sufficiently accurate.:1. Introduction 2 Basics of Solar Cells 3 Potential measurement by electron holography 4 Application of electron holography on solar cells 5 Design, construction, characterisation and application of a TEM holder for in-situ biasing and illumination 6 TEM sample preparation for in-situ biasing and illumination 7 Measurement of built-in potential under in-situ illumination and bias of solar cells / Photovoltaik bietet eine vielversprechende Energiequelle der Zukunft. Deshalb werden große Anstrengungen unternommen, um ihr Preis-Nutzen-Verhältnis zu verbessern. Neue Technologien und Materialien, wie poly-kristalline Materialien werden interessanter als mono-kristallines Silizium. Einige dieser Materialien beruhen auf der Basis von Kupfer-Chalkopyrit mit vorteilhaften Eigenschaften, wie direkt einstellbarer Bandlücke, hohen Absorptionskoeffizienten, niedrigen Abscheidetemperaturen und Verwendung von Low-Cost-Materialien. Allerdings ist die Korrelation zwischen den Eigenschaften der Dünnschicht-Materialien und der Leistung der Solarzellen noch nicht ausreichend verstanden, um die Effizienz weiter zu steigern. Hierfür muss ein umfassendes Verständnis der verschiedenen Phänomene wie der Rolle von Defekten, Dotierungskonzentrationen und Potenzialen erreicht werden, die die Entwicklung von innovativen Techniken für die Charakterisierung erfordert. Elektronen-Holographie kann zur Beantwortung dieser Fragen beitragen, weil sie die quantitative Rekonstruktion der komplexen Objektwelle im TEM erlaubt. Die Messung der Phase und der Amplitude der Welle macht es möglich, die Objektpotentiale zu bestimmen. Auf diese Weise wird Elektronen-Holographie ein leistungsfähiges Werkzeug für die Materialcharakterisierung im Nanometerbereich, weil sie Struktur und Potentialverteilung an derselben Stelle bestimmen kann. Doch können Artefakte und Missinterpretationen entstehen. Daher sind Aufzeichnung von Elektronenhologrammen sowie Rekonstruktion und Korrektur der Objektwelle von grundlegender Bedeutung für die Interpretation der Ergebnisse und werden im Detail vorgestellt. Ein spezielles Problem von polykristallinen Materialien ist die Tatsache, dass durch unterschiedlich orientierte Kristallite unterschiedliche Innere Potentiale gemessen werden können. Darüber hinaus besteht die Gefahr, dass die Elektronen mit unterschiedlichen Körnern in unterschiedlicher Weise dynamisch wechselwirken; dies führt zu Phasendifferezen, die erheblich stärker sein können als die eigentlich interessanten Halbleiterpotentiale. Deshalb werden die holographischen Untersuchungen so modifiziert, dass die Objekte in-situ, beispielsweise unter Anlegen elektrischer Spannungen (“biasing”) oder Beleuchtung mit Licht, untersucht werden. Die hierzu nötigen neuen Präparationsverfahren für die Objekte werden entwickelt. Ebenso werden neue in-situ Objekthalter entwickelt, die diese Parameter gezielt zu verändern gestatten. Als Ergebnis der Arbeit wird auch gezeigt, dass die Elektronenbeleuchtung einen wichtigen Einfluss auf die gemessenen Potentialverteilungen hat. Sie produziert größere Generationsraten von Elektronen-Loch-Paaren als 1 sun (Standard-Beleuchtung). Tatsächlich werden durch Rekombinationsprozesse an der Oberfläche der Probe die induzierten Potentiale in der Solarzelle verringert. Als Folge wird in der Regel nur das Potenzial des pn-Übergang gemessen. Um eine spürbare Wirkung durch Bestrahlung mit Licht zu erzeugen, muss die TEM-Lamelle dicker gewählt werden, und die Beleuchtung muss wesentlich intensiver sein als unter normalbedingungen. Diese Dissertation realisiert die erste umfassende Studie über die Anwendung von Elektronen-Holographie für die Messung von Potenzialen in Solarzellen unter Anwendung von Biasing und in-situ-Beleuchtung. Die experimentellen Befunde wurden mit umfangreichen Simulationsrechnungen verglichen. Diese zeigen, dass die Vorgänge im wesentlichen qualitativ verstanden sind, auch wenn sie die gemessenen Potentialverteilungen quantitativ oft noch nicht mit der erwünschten Genauigkeit wiedergeben.:1. Introduction 2 Basics of Solar Cells 3 Potential measurement by electron holography 4 Application of electron holography on solar cells 5 Design, construction, characterisation and application of a TEM holder for in-situ biasing and illumination 6 TEM sample preparation for in-situ biasing and illumination 7 Measurement of built-in potential under in-situ illumination and bias of solar cells