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Thema der Dissertation ist die Untersuchung von asymptotischen Eigenschaften im Wechselspiel von Diffusion und Wellenausbreitung. Es geht um diskrete, zufällige Schrödingeroperatoren, die in die diskrete Wärmeleitungsgleichung eingefügt werden. Das Ensemble der Lösungen kann mit der vom diskreten Laplace erzeugten Irrfahrt in kontinuierlicher Zeit und der Feynman-Kac-Formel stochastisch interpretiert werden. So werden Methoden aus der Theorie der großen Abweichungen anwendbar. Neben dem stochastischen Zugang können die Schrödingeroperatoren auch spektraltheoretisch untersucht werden. In der Dissertation wird das Wechselspiel dieser beiden Herangehensweisen im Hinblick auf die asymptotischen Eigenschaften der Momente, der integrierten Zustandsdichte und der Korrelationsfunktion betrachtet.

The heavy-tailed traffic from wireless users, caused by the emerging Internet and multimedia applications, induces extremely dynamic and variable network environment, which can fundamentally change the way in which wireless networks are conceived, designed, and operated. This thesis is concerned with modeling, analysis, and optimization of wireless networks in the presence of heavy tails. First, a novel traffic model is proposed, which captures the inherent relationship between the traffic dynamics and the joint effects of the mobility variability of network users and the spatial correlation in their observed physical phenomenon. Next, the asymptotic delay distribution of wireless users is analyzed under different traffic patterns and spectrum conditions, which reveals the critical conditions under which wireless users can experience heavy-tailed delay with significantly degraded QoS performance. Based on the delay analysis, the fundamental impact of heavy-tailed environment on network stability is studied. Specifically, a new network stability criterion, namely moment stability, is introduced to better characterize the QoS performance in the heavy-tailed environment. Accordingly, a throughput-optimal scheduling algorithm is proposed to maximize network throughput while guaranteeing moment stability. Furthermore, the impact of heavy-tailed spectrum on network connectivity is investigated. Towards this, the necessary conditions on the existence of delay-bounded connectivity are derived. To enhance network connectivity, the mobility-assisted data forwarding scheme is exploited, whose important design parameters, such as critical mobility radius, are derived. Moreover, the latency in wireless mobile networks is analyzed, which exhibits asymptotic linearity in the initial distance between mobile users.

Fifty years after the discovery of the first pulsating neutron star, the field of pulsar science has grown into a multidisciplinary research field, working to address a wide range of problems in astrophysics - from stellar evolution models to high precision tests of General Relativity to analysing the detailed structure of the Interstellar Medium in the Milky Way. Over 2500 Galactic pulsars have been discovered. The next generation telescopes, such as the Square Kilometre Array, promise to discover the complete observable Milky Way population, of several tens of thousands, over the next decade. These point sources in the sky have extreme properties, with matter densities comparable to that of an atomic nucleus, and surface magnetic fields a trillion times stronger than Earth's magnetic field. Observationally, the most valuable property is their rotational stability - allowing us to anticipate and sum their beamed radio emission, as the pulsar spins around its axis, on millisecond to second timescales. The detected radio wave signals carry with them information of the ionised interstellar medium (IISM) paths they traveled along. The imprints reveal that the pulsar signals we detect travel along multiple paths. While the bulk of the emitted signal propagates along a straight line, we also receive delayed emission scattered through small angles, back into our line of sight. This scattering is caused by fluctuations in the free electron densities of the IISM. The impact of these inhomogeneities is exaggerated at low observing frequencies, where averaged pulsar profiles are observed to be broadened, and showcase exponential scattering tails characterised by a scattering timescale г. Simple theoretical models predict a power law dependence of г on frequency, with a spectral index α = 4. Despite these predictions, my analysis of pulsar data in this thesis, reveal a more complex frequency dependence on г. I investigate the scattering characteristics of a set of pulsars observed by the Low Frequency Array (LOFAR), at 110~MHz to 190~MHz. These data are ideal datasets for accurate studies of pulsar scattering, providing broad frequency bands at low frequencies. I find anomalously low power law spectral indices, α, describing the frequency dependence of г. These indices are likely due to anisotropic scattering mechanisms or small scattering clouds in the IISM. To conduct effective data analysis, I develop scattering fitting techniques by first analysing IISM effects on simulated pulsar data. I investigate the effects of two different types of scattering mechanisms, isotropic and anisotropic scattering, and consider each of their particular frequency-dependent impacts on pulsar data. The work on simulated data provides a robust fitting technique for extracting scattering parameters and a framework for the interpretation of the LOFAR data used in this study. The fitting technique simultaneously models scattering effects and standard frequency-dependent pulse profile evolution. I present results for 13 pulsars with simple pulse shapes, and find that г, associated with scattering by a single thin screen, has a power law dependence on frequency with α ranging from 1.50 to 4.0. My results show that extremely anisotropic scattering can cause low α measurements. The anomalous scattering properties can also be caused by the presence of small scattering clumps in the IISM, as opposed to the conventionally modelled large scattering screens. Evidence for both anisotropic scattering and small scattering clouds with high electron densities come from other areas of research. Indications of the anisotropic nature of the local IISM mostly come from high resolution pulsar scintillation analyses, while evidence for high density scattering clouds is often based on extreme scattering events measured through quasar observations. My results suggest that these anomalous scattering properties are more prevalent than formerly thought, prompting us to reconsider the physical conditions of the IISM, where traditionally high electron densities are reserved for H_II regions and anisotropy is not modelled. High quality, low frequency pulsar data, where anomalous propagation effects become measurable, are a valuable addition in assisting us to distinguish between the different physical mechanisms that can be at play. The more complex these IISM characteristics reveal themselves to be, the harder it will be to disentangle intrinsic profile emission from IISM propagation imprints. Successfully separating these effects, however, promises to improve our understanding of the intrinsic pulsar radio emission - a process that is still poorly understood.

The aim of this thesis is to show that the use of heavy-tailed distributions in finance is theoretically unfounded and may cause significant misunderstandings and fallacies in model interpretation. The main reason seems to be a wrong understanding of the concept of the distributional tail. Also in models based on real data it seems more reasonable to concentrate on the central part of the distribution not tails. Powered by TCPDF (www.tcpdf.org)

<div> Challenges in the semiconductor industry have resulted in the discovery of a plethora of promising materials and devices such as the III-Vs (InGaAs, GaSb, GaN/InGaN) and 2D materials (Transition-metal dichalcogenides [TMDs]) with wide-ranging applications from logic devices, optoelectronics to biomedical devices. Performance of these devices suffer significantly from scattering processes such as polar-optical phonons (POP), charged impurities and remote phonon scattering. These scattering mechanisms are long-ranged, and a quantitative description of such devices require non-local scattering calculations that are computationally expensive. Though there have been extensive studies on coherent transport in these materials, simulations are scarce with scattering and virtually non-existent with non-local scattering. </div><div> </div><div>In this work, these scattering mechanisms with full non-locality are treated rigorously within the Non-Equilibrium Green's function (NEGF) formalism. Impact of non-locality on charge transport is assessed for GaSb/InAs nanowire TFETs highlighting the underestimation of scattering with local approximations. Phonon, impurity scattering, and structural disorders lead to exponentially decaying density of states known as Urbach tails/band tails. Impact of such scattering mechanisms on the band tail is studied in detail for several bulk and confined III-V devices (GaAs, InAs, GaSb and GaN) showing good agreement with existing experimental data. A systematic study of the dependence of Urbach tails with dielectric environment (oxides, charged impurities) is performed for single and multilayered 2D TMDs (MoS2, WS2 and WSe2) providing guideline values for researchers. </div><div><br></div><div>Often, empirical local approximations (ELA) are used in the literature to capture these non-local scattering processes. A comparison against ELA highlight the need for non-local scattering. A physics-based local approximation model is developed that captures the essential physics and is computationally feasible.</div>

Juraj Bodík Abstract This thesis is dealing with the following problem: Let us have two stationary time series with heavy- tailed marginal distributions. We want to detect whether they have a causal relation, i.e. if a change in one of them causes a change in the other. The question of distinguishing between causality and correlation is essential in many different science fields. Usual methods for causality detection are not well suited if the causal mechanisms only manifest themselves in extremes. In this thesis, we propose a new method that can help us in such a nontraditional case distinguish between correlation and causality. We define the so-called causal tail coefficient for time series, which, under some assumptions, correctly detects the asymmetrical causal relations between different time series. We will rigorously prove this claim, and we also propose a method on how to statistically estimate the causal tail coefficient from a finite number of data. The advantage is that this method works even if nonlinear relations and common ancestors are present. Moreover, we will mention how our method can help detect a time delay between the two time series. We will show how our method performs on some simulations. Finally, we will show on a real dataset how this method works, discussing a cause of...

<p>The Artillery Lake area is diagonally bisected by the north-northeasterly trending Thelon Front. The best single surface feature to represent the Thelon Front is the "straight zone" which is a zone of porphyroclastic metasediments that also contains the study area. Kinematic indicators observed in the study area include extensional shear surfaces, C&S fabric, mica "fish", asymmetrical porphyroclast tails, asymmetrical folds, microfaulted porphyroclasts and secondary quartz subgrain foliations. Kinematic analysis of these features has shown that right lateral simple shear displacements and "east-side-up" vertical shear displacements have been accommodated within the rocks of the study area. The displacement senses determined by kinematic analysis are consistent with the regional data indicating progressively deeper exposures of structural levels to the east which suggests vertical motions localized at the domain boundaries. The stretching lineation present in the area is a combination of passive and direct extensions due to sub-vertical motions in the shear zone. A transition from early-ductile to late-brittle feldspar deformation textures indicates that metamorphic conditions during initial deformation were at epidoteamphibolite facies and relaxed during the later stages of deformation to greenschist facies. </p> / Thesis / Bachelor of Science (BSc)

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Le modèle d'accrochage de polymère décrit le comportement d'une chaîne de Markov en interaction avec un état donné. Cette interaction peut attirer ou repousser la chaîne de Markov et elle est modulée par deux paramètres, h et β. Quand β = 0 on parle de modèle homogène, qui est complètement solvable. Le modèle désordonné, i.e. quand β > 0, est mathématiquement le plus intéressant. Dans ce cas, l'interaction dépend d'une source d'aléa extérieur indépendant de la chaîne de Markov, appelée désordre. L'interaction est réalisée en modifiant la loi originelle de la chaîne de Markov par une mesure de Gibbs et la probabilité obtenue définit le modèle d'accrochage de polymère. Le but principal est d'étudier et de comprendre la structure des trajectoires typiques de la chaîne de Markov sous cette nouvelle probabilité. Le premier sujet de recherche concerne le modèle d'accrochage de polymère où le désordre est à queues lourdes et où le temps de retour de la chaîne de Markov suit une distribution sous-exponentielle. Dans notre deuxième résultat nous étudions le modèle d'accrochage de polymère avec un désordre à queues légères et le temps de retour de la chaîne de Markov avec une distribution à queues polynomiales d'exposant α > 0. On peut démontrer qu'il existe un point critique, h(β). Notre but est comprendre le comportement du point critique quand β -> 0. La réponse dépend de la valeur de α. Dans la littérature on a des résultats précis pour α < ½ et α > 1. Nous montrons que α ∈ (1/2, 1) le comportement du modèle dans la limite du désordre faible est universel et le point critique, opportunément changé d'échelle, converge vers la même quantité donnée par un modèle continu / The pinning model describes the behavior of a Markov chain in interaction with a distinguished state. This interaction can attract or repel the Markov chain path with a force tuned by two parameters, h and β. If β = 0 we obtain the homogeneous pinning model, which is completely solvable. The disordered pinning model, i.e. when β > 0, is most challenging and mathematically interesting. In this case the interaction depends on an external source of randomness, independent of the Markov chain, called disorder. The interaction is realized by perturbing the original Markov chain law via a Gibbs measure, which defines the Pinning Model. Our main aim is to understand the structure of a typical Markov chain path under this new probability measure. The first research topic of this thesis is the pinning model in which the disorder is heavy-tailed and the return times of the Markov chain have a sub-exponential distribution. In our second result we consider a pinning model with a light-tailed disorder and the return times of the Markov chain with a polynomial tail distribution, with exponent α > 0. It is possible to show that there exists a critical point, h(β). Our goal is to understand the behavior of the critical point when β -> 0. The answer depends on the value of α and in the literature there are precise results only for the case α < ½ et α > 1. We show that for α ∈ (1/2, 1) the behavior of the pinning model in the weak disorder limit is universal and the critical point, suitably rescaled, converges to the related quantity of a continuum model