TY - THES
AB - This thesis is concerned with the inference of current population structure based on geo-referenced genetic data. The underlying idea is that population structure affects its spatial genetic structure. Therefore, genotype information can be utilized to estimate important demographic parameters such as migration rates. These indirect estimates of population structure have become very attractive, as genotype data is now widely available. However, there also has been much concern about these approaches. Importantly, genetic structure can be influenced by many complex patterns, which often cannot be disentangled. Moreover, many methods merely fit heuristic patterns of genetic structure, and do not build upon population genetics theory. Here, I describe two novel inference methods that address these shortcomings. In Chapter 2, I introduce an inference scheme based on a new type of signal, identity by descent (IBD) blocks. Recently, it has become feasible to detect such long blocks of genome shared between pairs of samples. These blocks are direct traces of recent coalescence events. As such, they contain ample signal for inferring recent demography. I examine sharing of IBD blocks in two-dimensional populations with local migration. Using a diffusion approximation, I derive formulas for an isolation by distance pattern of long IBD blocks and show that sharing of long IBD blocks approaches rapid exponential decay for growing sample distance. I describe an inference scheme based on these results. It can robustly estimate the dispersal rate and population density, which is demonstrated on simulated data. I also show an application to estimate mean migration and the rate of recent population growth within Eastern Europe. Chapter 3 is about a novel method to estimate barriers to gene flow in a two dimensional population. This inference scheme utilizes geographically localized allele frequency fluctuations - a classical isolation by distance signal. The strength of these local fluctuations increases on average next to a barrier, and there is less correlation across it. I again use a framework of diffusion of ancestral lineages to model this effect, and provide an efficient numerical implementation to fit the results to geo-referenced biallelic SNP data. This inference scheme is able to robustly estimate strong barriers to gene flow, as tests on simulated data confirm.
AU - Ringbauer, Harald
ID - 200
TI - Inferring recent demography from spatial genetic structure
ER -
TY - THES
AB - We describe arrangements of three-dimensional spheres from a geometrical and topological point of view. Real data (fitting this setup) often consist of soft spheres which show certain degree of deformation while strongly packing against each other. In this context, we answer the following questions: If we model a soft packing of spheres by hard spheres that are allowed to overlap, can we measure the volume in the overlapped areas? Can we be more specific about the overlap volume, i.e. quantify how much volume is there covered exactly twice, three times, or k times? What would be a good optimization criteria that rule the arrangement of soft spheres while making a good use of the available space? Fixing a particular criterion, what would be the optimal sphere configuration? The first result of this thesis are short formulas for the computation of volumes covered by at least k of the balls. The formulas exploit information contained in the order-k Voronoi diagrams and its closely related Level-k complex. The used complexes lead to a natural generalization into poset diagrams, a theoretical formalism that contains the order-k and degree-k diagrams as special cases. In parallel, we define different criteria to determine what could be considered an optimal arrangement from a geometrical point of view. Fixing a criterion, we find optimal soft packing configurations in 2D and 3D where the ball centers lie on a lattice. As a last step, we use tools from computational topology on real physical data, to show the potentials of higher-order diagrams in the description of melting crystals. The results of the experiments leaves us with an open window to apply the theories developed in this thesis in real applications.
AU - Iglesias Ham, Mabel
ID - 201
TI - Multiple covers with balls
ER -
TY - THES
AB - Nowadays, quantum computation is receiving more and more attention as an alternative to the classical way of computing. For realizing a quantum computer, different devices are investigated as potential quantum bits. In this thesis, the focus is on Ge hut wires, which turned out to be promising candidates for implementing hole spin quantum bits. The advantages of Ge as a material system are the low hyperfine interaction for holes and the strong spin orbit coupling, as well as the compatibility with the highly developed CMOS processes in industry. In addition, Ge can also be isotopically purified which is expected to boost the spin coherence times. The strong spin orbit interaction for holes in Ge on the one hand enables the full electrical control of the quantum bit and on the other hand should allow short spin manipulation times. Starting with a bare Si wafer, this work covers the entire process reaching from growth over the fabrication and characterization of hut wire devices up to the demonstration of hole spin resonance. From experiments with single quantum dots, a large g-factor anisotropy between the in-plane and the out-of-plane direction was found. A comparison to a theoretical model unveiled the heavy-hole character of the lowest energy states. The second part of the thesis addresses double quantum dot devices, which were realized by adding two gate electrodes to a hut wire. In such devices, Pauli spin blockade was observed, which can serve as a read-out mechanism for spin quantum bits. Applying oscillating electric fields in spin blockade allowed the demonstration of continuous spin rotations and the extraction of a lower bound for the spin dephasing time. Despite the strong spin orbit coupling in Ge, the obtained value for the dephasing time is comparable to what has been recently reported for holes in Si. All in all, the presented results point out the high potential of Ge hut wires as a platform for long-lived, fast and fully electrically tunable hole spin quantum bits.
AU - Watzinger, Hannes
ID - 49
TI - Ge hut wires - from growth to hole spin resonance
ER -
TY - THES
AB - In this thesis we will discuss systems of point interacting fermions, their stability and other spectral properties. Whereas for bosons a point interacting system is always unstable this ques- tion is more subtle for a gas of two species of fermions. In particular the answer depends on the mass ratio between these two species. Most of this work will be focused on the N + M model which consists of two species of fermions with N, M particles respectively which interact via point interactions. We will introduce this model using a formal limit and discuss the N + 1 system in more detail. In particular, we will show that for mass ratios above a critical one, which does not depend on the particle number, the N + 1 system is stable. In the context of this model we will prove rigorous versions of Tan relations which relate various quantities of the point-interacting model. By restricting the N + 1 system to a box we define a finite density model with point in- teractions. In the context of this system we will discuss the energy change when introducing a point-interacting impurity into a system of non-interacting fermions. We will see that this change in energy is bounded independently of the particle number and in particular the bound only depends on the density and the scattering length. As another special case of the N + M model we will show stability of the 2 + 2 model for mass ratios in an interval around one. Further we will investigate a different model of point interactions which was discussed before in the literature and which is, contrary to the N + M model, not given by a limiting procedure but is based on a Dirichlet form. We will show that this system behaves trivially in the thermodynamic limit, i.e. the free energy per particle is the same as the one of the non-interacting system.
AU - Moser, Thomas
ID - 52
TI - Point interactions in systems of fermions
ER -
TY - THES
AB - The most common assumption made in statistical learning theory is the assumption of the independent and identically distributed (i.i.d.) data. While being very convenient mathematically, it is often very clearly violated in practice. This disparity between the machine learning theory and applications underlies a growing demand in the development of algorithms that learn from dependent data and theory that can provide generalization guarantees similar to the independent situations. This thesis is dedicated to two variants of dependencies that can arise in practice. One is a dependence on the level of samples in a single learning task. Another dependency type arises in the multi-task setting when the tasks are dependent on each other even though the data for them can be i.i.d. In both cases we model the data (samples or tasks) as stochastic processes and introduce new algorithms for both settings that take into account and exploit the resulting dependencies. We prove the theoretical guarantees on the performance of the introduced algorithms under different evaluation criteria and, in addition, we compliment the theoretical study by the empirical one, where we evaluate some of the algorithms on two real world datasets to highlight their practical applicability.
AU - Zimin, Alexander
ID - 68
TI - Learning from dependent data
ER -
TY - THES
AB - A qubit, a unit of quantum information, is essentially any quantum mechanical two-level system which can be coherently controlled. Still, to be used for computation, it has to fulfill criteria. Qubits, regardless of the system in which they are realized, suffer from decoherence. This leads to loss of the information stored in the qubit. The upper bound of the time scale on which decoherence happens is set by the spin relaxation time. In this thesis I studied a two-level system consisting of a Zeeman-split hole spin confined in a quantum dot formed in a Ge hut wire. Such Ge hut wires have emerged as a promising material system for the realization of spin qubits, due to the combination of two significant properties: long spin coherence time as expected for group IV semiconductors due to the low hyperfine interaction and a strong valence band spin-orbit coupling. Here, I present how to fabricate quantum dot devices suitable for electrical transport measurements. Coupled quantum dot devices allowed the realization of a charge sensor, which is electrostatically and tunnel coupled to a quantum dot. By integrating the charge sensor into a radio-frequency reflectometry setup, I performed for the first time single-shot readout measurements of hole spins and extracted the hole spin relaxation times in Ge hut wires.
AU - Vukušić, Lada
ID - 69
TI - Charge sensing and spin relaxation times of holes in Ge hut wires
ER -
TY - THES
AB - The eigenvalue density of many large random matrices is well approximated by a deterministic measure, the self-consistent density of states. In the present work, we show this behaviour for several classes of random matrices. In fact, we establish that, in each of these classes, the self-consistent density of states approximates the eigenvalue density of the random matrix on all scales slightly above the typical eigenvalue spacing. For large classes of random matrices, the self-consistent density of states exhibits several universal features. We prove that, under suitable assumptions, random Gram matrices and Hermitian random matrices with decaying correlations have a 1/3-Hölder continuous self-consistent density of states ρ on R, which is analytic, where it is positive, and has either a square root edge or a cubic root cusp, where it vanishes. We, thus, extend the validity of the corresponding result for Wigner-type matrices from [4, 5, 7]. We show that ρ is determined as the inverse Stieltjes transform of the normalized trace of the unique solution m(z) to the Dyson equation −m(z) −1 = z − a + S[m(z)] on C N×N with the constraint Im m(z) ≥ 0. Here, z lies in the complex upper half-plane, a is a self-adjoint element of C N×N and S is a positivity-preserving operator on C N×N encoding the first two moments of the random matrix. In order to analyze a possible limit of ρ for N → ∞ and address some applications in free probability theory, we also consider the Dyson equation on infinite dimensional von Neumann algebras. We present two applications to random matrices. We first establish that, under certain assumptions, large random matrices with independent entries have a rotationally symmetric self-consistent density of states which is supported on a centered disk in C. Moreover, it is infinitely often differentiable apart from a jump on the boundary of this disk. Second, we show edge universality at all regular (not necessarily extreme) spectral edges for Hermitian random matrices with decaying correlations.
AU - Alt, Johannes
ID - 149
TI - Dyson equation and eigenvalue statistics of random matrices
ER -
TY - THES
AB - The aim of this thesis was the development of new strategies for optical and optogenetic control of proliferative and pro-survival signaling, and characterizing them from the molecular mechanism up to cellular effects. These new light-based methods have unique features, such as red light as an activator, or the avoidance of gene delivery, which enable to overcome current limitations, such as light delivery to target tissues and feasibility as therapeutic approach. A special focus was placed on implementing these new light-based approaches in pancreatic β-cells, as β-cells are the key players in diabetes and especially their loss in number negatively affects disease progression. Currently no treatment options are available to compensate the lack of functional β-cells in diabetic patients.
In a first approach, red-light-activated growth factor receptors, in particular receptor tyrosine kinases were engineered and characterized. Receptor activation with light allows spatio-temporal control compared to ligand-based activation, and especially red light exhibits deeper tissue penetration than other wavelengths of the visible spectrum. Red-light-activated receptor tyrosine kinases robustly activated major growth factor related signaling pathways with a high temporal resolution. Moreover, the remote activation of the proliferative MAPK/Erk pathway by red-light-activated receptor tyrosine kinases in a pancreatic β-cell line was also achieved, through one centimeter thick mouse tissue. Although red-light-activated receptor tyrosine kinases are particularly attractive for applications in animal models due to the deep tissue penetration of red light, a drawback, especially with regard to translation into humans, is the requirement of gene therapy.
In a second approach an endogenous light-sensitive mechanism was identified and its potential to promote proliferative and pro-survival signals was explored, towards light-based tissue regeneration without the need for gene transfer. Blue-green light illumination was found to be sufficient for the activation of proliferation and survival promoting signaling pathways in primary pancreatic murine and human islets. Blue-green light also led to an increase in proliferation of primary islet cells, an effect which was shown to be mostly β-cell specific in human islets. Moreover, it was demonstrated that this approach of pancreatic β-cell expansion did not have any negative effect on the β-cell function, in particular on their insulin secretion capacity. In contrast, a trend for enhanced insulin secretion under high glucose conditions after illumination was detected. In order to unravel the detailed characteristics of this endogenous light-sensitive mechanism, the precise light requirements were determined. In addition, the expression of light sensing proteins, OPN3 and rhodopsin, was detected. The observed effects were found to be independent of handling effects such as temperature differences and cytochrome c oxidase dependent ATP increase, but they were found to be enhanced through the knockout of OPN3. The exact mechanism of how islets cells sense light and the identity of the photoreceptor remains unknown.
Summarized two new light-based systems with unique features were established that enable the activation of proliferative and pro-survival signaling pathways. While red-light-activated receptor tyrosine kinases open a new avenue for optogenetics research, by allowing non-invasive control of signaling in vivo, the identified endogenous light-sensitive mechanism has the potential to be the basis of a gene therapy-free therapeutical approach for light-based β-cell expansion.
AU - Gschaider-Reichhart, Eva
ID - 418
TI - Optical and optogenetic control of proliferation and survival
ER -
TY - THES
AB - Neuronal networks in the brain consist of two main types of neuron, glutamatergic principal neurons and GABAergic interneurons. Although these interneurons only represent 10–20% of the whole population, they mediate feedback and feedforward inhibition and are involved in the generation of high-frequency network oscillations. A hallmark functional property of GABAergic interneurons, especially of the parvalbumin‑expressing (PV+) subtypes, is the speed of signaling at their output synapse across species and brain regions. Several molecular and subcellular factors may underlie the submillisecond signaling at GABAergic synapses. Such as the selective use of P/Q type Ca2+ channels and the tight coupling between Ca2+ channels and Ca2+ sensors of exocytosis. However, whether the molecular identity of the release sensor contributes to these signaling properties remains unclear. Besides, these interneurons are mainly show depression in response to train of stimuli. How could they keep sufficient release to control the activity of postsynaptic principal neurons during high network activity, is largely elusive. For my Ph.D. work, we firstly examined the Ca2+ sensor of exocytosis at the GABAergic basket cell (BC) to Purkinje cell (PC) synapse in the cerebellum. Immunolabeling suggested that BC terminals selectively expressed synaptotagmin 2 (Syt2), whereas synaptotagmin 1 (Syt1) was enriched in excitatory terminals. Genetic elimination of Syt2 reduced action potential-evoked release to ~10% compared to the wild-type control, identifying Syt2 as the major Ca2+ sensor at BC‑PC synapses. Differential adenovirus-mediated rescue revealed Syt2 triggered release with shorter latency and higher temporal precision, and mediated faster vesicle pool replenishment than Syt1. Furthermore, deletion of Syt2 severely reduced and delayed disynaptic inhibition following parallel fiber stimulation. Thus, the selective use of Syt2 as the release sensor at BC–PC synapse ensures fast feedforward inhibition in cerebellar microcircuits. Additionally, we tested the function of another synaptotagmin member, Syt7, for inhibitory synaptic transmission at the BC–PC synapse. Syt7 is thought to be a Ca2+ sensor that mediates asynchronous transmitter release and facilitation at synapses. However, it is strongly expressed in fast-spiking, PV+ GABAergic interneurons and the output synapses of these neurons produce only minimal asynchronous release and show depression rather than facilitation. How could Syt7, a facilitation sensor, contribute to the depressed inhibitory synaptic transmission needs to be further investigated and understood. Our results indicated that at the BC–PC synapse, Syt7 contributes to asynchronous release, pool replenishment and facilitation. In combination, these three effects ensure efficient transmitter release during high‑frequency activity and guarantee frequency independence of inhibition. Taken together, our results confirmed that Syt2, which has the fastest kinetic properties among all synaptotagmin members, is mainly used by the inhibitory BC‑PC synapse for synaptic transmission, contributing to the speed and temporal precision of transmitter release. Furthermore, we showed that Syt7, another highly expressed synaptotagmin member in the output synapses of cerebellar BCs, is used for ensuring efficient inhibitor synaptic transmission during high activity.
AU - Chen, Chong
ID - 324
TI - Synaptotagmins ensure speed and efficiency of inhibitory neurotransmitter release
ER -
TY - THES
AB - Antibiotic resistance can emerge spontaneously through genomic mutation and render treatment ineffective. To counteract this process, in addition to the discovery and description of resistance mechanisms,a deeper understanding of resistanceevolvabilityand its determinantsis needed. To address this challenge, this thesisuncoversnew genetic determinants of resistance evolvability using a customized robotic setup, exploressystematic ways in which resistance evolution is perturbed due to dose-responsecharacteristics of drugs and mutation rate differences,and mathematically investigates the evolutionary fate of one specific type of evolvability modifier -a stress-induced mutagenesis allele.We find severalgenes which strongly inhibit or potentiate resistance evolution. In order to identify them, we first developedan automated high-throughput feedback-controlled protocol whichkeeps the population size and selection pressure approximately constant for hundreds of cultures by dynamically re-diluting the cultures and adjusting the antibiotic concentration. We implementedthis protocol on a customized liquid handling robot and propagated 100 different gene deletion strains of Escherichia coliin triplicate for over 100 generations in tetracycline and in chloramphenicol, and comparedtheir adaptation rates.We find a diminishing returns pattern, where initially sensitive strains adapted more compared to less sensitive ones. Our data uncover that deletions of certain genes which do not affect mutation rate,including efflux pump components, a chaperone and severalstructural and regulatory genes can strongly and reproducibly alterresistance evolution. Sequencing analysis of evolved populations indicates that epistasis with resistance mutations is the most likelyexplanation. This work could inspire treatment strategies in which targeted inhibitors of evolvability mechanisms will be given alongside antibiotics to slow down resistance evolution and extend theefficacy of antibiotics.We implemented astochasticpopulation genetics model, toverifyways in which general properties, namely, dose-response characteristics of drugs and mutation rates, influence evolutionary dynamics. In particular, under the exposure to antibiotics with shallow dose-response curves,bacteria have narrower distributions of fitness effects of new mutations. We show that in silicothis also leads to slower resistance evolution. We see and confirm with experiments that increased mutation rates, apart from speeding up evolution, also leadto high reproducibility of phenotypic adaptation in a context of continually strong selection pressure.Knowledge of these patterns can aid in predicting the dynamics of antibiotic resistance evolutionand adapting treatment schemes accordingly.Focusing on a previously described type of evolvability modifier –a stress-induced mutagenesis allele –we find conditions under which it can persist in a population under periodic selectionakin to clinical treatment. We set up a deterministic infinite populationcontinuous time model tracking the frequencies of a mutator and resistance allele and evaluate various treatment schemes in how well they maintain a stress-induced mutator allele. In particular,a high diversity of stresses is crucial for the persistence of the mutator allele. This leads to a general trade-off where exactly those diversifying treatment schemes which are likely to decrease levels of resistance could lead to stronger selection of highly evolvable genotypes.In the long run, this work will lead to a deeper understanding of the genetic and cellular mechanisms involved in antibiotic resistance evolution and could inspire new strategies for slowing down its rate.
AU - Lukacisinova, Marta
ID - 6263
TI - Genetic determinants of antibiotic resistance evolution
ER -