@phdthesis{149,
abstract = {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.},
author = {Alt, Johannes},
pages = {456},
publisher = {IST Austria},
title = {{Dyson equation and eigenvalue statistics of random matrices}},
doi = {10.15479/AT:ISTA:TH_1040},
year = {2018},
}
@phdthesis{50,
abstract = {The Wnt/planar cell polarity (Wnt/PCP) pathway determines planar polarity of epithelial cells in both vertebrates and invertebrates. The role that Wnt/PCP signaling plays in mesenchymal contexts, however, is only poorly understood. While previous studies have demonstrated the capacity of Wnt/PCP signaling to polarize and guide directed migration of mesenchymal cells, it remains unclear whether endogenous Wnt/PCP signaling performs these functions instructively, as it does in epithelial cells. Here we developed a light-switchable version of the Wnt/PCP receptor Frizzled 7 (Fz7) to unambiguously distinguish between an instructive and a permissive role of Wnt/PCP signaling for the directional collective migration of mesendoderm progenitor cells during zebrafish gastrulation. We show that prechordal plate (ppl) cell migration is defective in maternal-zygotic fz7a and fz7b (MZ fz7a,b) double mutant embryos, and that Fz7 functions cell-autonomously in this process by promoting ppl cell protrusion formation and directed migration. We further show that local activation of Fz7 can direct ppl cell migration both in vitro and in vivo. Surprisingly, however, uniform Fz7 activation is sufficient to fully rescue the ppl cell migration defect in MZ fz7a,b mutant embryos, indicating that Wnt/PCP signaling functions permissively rather than instructively in directed mesendoderm cell migration during zebrafish gastrulation.},
author = {Capek, Daniel},
pages = {95},
publisher = {IST Austria},
title = {{Optogenetic Frizzled 7 reveals a permissive function of Wnt/PCP signaling in directed mesenchymal cell migration}},
doi = {10.15479/AT:ISTA:TH_1031},
year = {2018},
}
@phdthesis{68,
abstract = {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.},
author = {Zimin, Alexander},
pages = {92},
publisher = {IST Austria},
title = {{Learning from dependent data}},
doi = {10.15479/AT:ISTA:TH1048},
year = {2018},
}
@phdthesis{51,
abstract = {Asymmetries have long been known about in the central nervous system. From gross anatomical differences, such as the presence of the parapineal organ in only one hemisphere of the developing zebrafish, to more subtle differences in activity between both hemispheres, as seen in freely roaming animals or human participants under PET and fMRI imaging analysis. The presence of asymmetries has been demonstrated to have huge behavioural implications, with their disruption often leading to the generation of neurological disorders, memory problems, changes in personality, and in an organism's health and well-being. For my Ph.D. work I aimed to tackle two important avenues of research. The first being the process of input-side dependency in the hippocampus, with the goal of finding a key gene responsible for its development (Gene X). The second project was to do with experience-induced laterality formation in the hippocampus. Specifically, how laterality in the synapse density of the CA1 stratum radiatum (s.r.) could be induced purely through environmental enrichment. Through unilateral tracer injections into the CA3, I was able to selectively measure the properties of synapses within the CA1 and investigate how they differed based upon which hemisphere the presynaptic neurone originated. Having found the existence of a previously unreported reversed (left-isomerism) i.v. mutant, through morpholocal examination of labelled terminals in the CA1 s.r., I aimed to elucidate a key gene responsible for the process of left or right determination of inputs to the CA1 s.r.. This work relates to the previous finding of input-side dependent asymmetry in the wild-type rodent, where the origin of the projecting neurone to the CA1 will determine the morphology of a synapse, to a greater degree than the hemisphere in which the projection terminates. Using left- and right-isomerism i.v. mice, in combination with whole genome sequence analysis, I highlight Ena/VASP-like (Evl) as a potential target for Gene X. In relation to this topic, I also highlight my work in the recently published paper of how knockout of PirB can lead to a lack of input-side dependency in the murine hippocampus. For the second question, I show that the environmental enrichment paradigm will lead to an asymmetry in the synapse densities in the hippocampus of mice. I also highlight that the nature of the enrichment is of less consequence than the process of enrichment itself. I demonstrate that the CA3 region will dramatically alter its projection targets, in relation to environmental stimulation, with the asymmetry in synaptic density, caused by enrichment, relying heavily on commissural fibres. I also highlight the vital importance of input-side dependent asymmetry, as a necessary component of experience-dependent laterality formation in the CA1 s.r.. However, my results suggest that it isn't the only cause, as there appears to be a CA1 dependent mechanism also at play. Upon further investigation, I highlight the significant, and highly important, finding that the changes seen in the CA1 s.r. were predominantly caused through projections from the left-CA3, with the right-CA3 having less involvement in this mechanism.},
author = {Case, Matthew J},
pages = {186},
publisher = {IST Austria},
title = {{From the left to the right: A tale of asymmetries, environments, and hippocampal development}},
doi = {10.15479/AT:ISTA:th_1032},
year = {2018},
}
@phdthesis{69,
abstract = {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.},
author = {Vukušić, Lada},
pages = {103},
publisher = {IST Austria},
title = {{Charge sensing and spin relaxation times of holes in Ge hut wires}},
doi = {10.15479/AT:ISTA:TH_1047},
year = {2018},
}