abstract: Deep neural networks (DNNs) have had tremendous success in a variety of statistical learning applications due to their vast expressive power. Most applications run DNNs on the cloud on parallelized architectures. There is a need for for efficient DNN inference on edge with low precision hardware and analog accelerators. To make trained models more robust for this setting, quantization and analog compute noise are modeled as weight space perturbations to DNNs and an information theoretic regularization scheme is used to penalize the KL-divergence between perturbed and unperturbed models. This regularizer has similarities to both natural gradient descent and knowledge distillation, but has the advantage of explicitly promoting the network to and a broader minimum that is robust to weight space perturbations. In addition to the proposed regularization, KL-divergence is directly minimized using knowledge distillation. Initial validation on FashionMNIST and CIFAR10 shows that the information theoretic regularizer and knowledge distillation outperform existing quantization schemes based on the straight through estimator or L2 constrained quantization. / Dissertation/Thesis / Masters Thesis Computer Engineering 2019

"Dynamics" is very roughly the study of how objects change in time; for instance whether an electrical circuit goes to equilibrium, due to thermal dissipation. By "information", we mean how helpful it is to observe an object in order to know it better, for instance how many binary digits we can acquire on the value of a voltage by an appropriate measure. A "computation" is a physical process, e.g. the flow of current into a complex set of transistors, that after some time eventually gives us the solution of a mathematical problem (such as "Is 13 prime?"). We are interested to various relations between these concepts. In a first chapter, we unify some arguments in the literature to show that a whole class of quantities of dynamical systems are uncomputable. For instance the topological entropy of tilings and Turing machines. Then we propose a precise meaning to the statement "This dynamical system is a computer", at least for symbolic systems, such as cellular automata. We also show, for instance, that a "computer" must be dynamically unstable, and can even be chaotic. In a third chapter, we compare how complicated it is to control a system according whether we can acquire information on it ("feedback") or not ("open loop"). We are specifically interested in finite-state systems. In last chapter we show how to control a scalar linear system when only a finite amount of information can be acquired at every step of time.

Electron transport in mesoscopic systems, such as quantum point contacts and Aharonov-Bohm rings are investigated numerically in a tight-binding language with a recursive Green's function algorithm. The simulation reveals among other things the quantized nature of the conductance in point contacts, the Hall conductance, the decreasing sensitivity to scattering impurities in a magnetic field, and the periodic magnetoconductance in an Aharonov-Bohm ring. Furthermore, the probability density distributions for some different setups are mapped, making the transmission coefficients, the quantum Hall effect, and the cyclotron radius visible, where the latter indicates the correspondance between quantum mechanics and classical physics on the mesoscopic scale.

The aim of the study presented in this thesis is to explore the electrical and physical properties of films of tin and lead clusters. Understanding the novel conductance properties of cluster films and related phenomenon such as coalescence is important to fabricate any cluster based devices. Coalescence is an important phenomenon in metallic cluster films. Due to coalescence the morphology of the films changes with time which changes their properties and could lead to failure in cluster devices. Coalescence is studied in Sn and Pb cluster films deposited on Si$_3$N$_4$ surfaces using Ultra High Vacuum (UHV) cluster deposition system. The conductance of the overall film is linked to the conductance of the individual necks between clusters by simulations. It is observed that the coalescence process in Sn and Pb films follows a power law in time with an exponent smaller than reported in literature. These results are substantiated by the results from previous experimental and Kinetic Monte Carlo (KMC) simulation studies at UC. Percolating films of Sn show unique conductance properties. These films are characterized using various electrode configurations, applied voltages and temperatures. The conductance measurements are performed by depositing clusters on prefabricated gold electrodes on top of Si$_3$N$_4$ substrates. Sn cluster films exhibit a variety of conductance behaviours during and after the end of deposition. It is observed that the evolution of conductance during the onsets at percolation threshold is dependent on the film morphology. Samples showing difference responses in onset also behave differently after the end of deposition. Therefore all samples were categorized according to their onset behaviour. After the end of deposition, when a bias voltage is applied, the conductance of Sn films steps up and down between various well-defined conductance levels. It is also observed that in many cases the conductance levels between which these devices jump are close to integral multiples of the conductance quantum. There are many possible explanations for the steps in conductance. One of the explanations is formation and breaking of conducting paths in the cluster films by electric field induced evaporation and electromigration respectively. The stepping behaviour is similar to that in non-volatile memory devices and hence very interesting to explore due to potential applications.

We numerically study the dynamics and interactions of vortex rings in the nonlinear Schrödinger equation (NLSE). Single ring dynamics for both bright and dark vortex rings are explored including their traverse velocity, stability, and perturbations resulting in quadrupole oscillations. Multi-ring dynamics of dark vortex rings are investigated, including scattering and merging of two colliding rings, leapfrogging interactions of co-traveling rings, as well as co-moving steady-state multi-ring ensembles. Simulations of choreographed multi-ring setups are also performed, leading to intriguing interaction dynamics. Due to the inherent lack of a close form solution for vortex rings and the dimensionality where they live, efficient numerical methods to integrate the NLSE have to be developed in order to perform the extensive number of required simulations. To facilitate this, compact high-order numerical schemes for the spatial derivatives are developed which include a new semi-compact modulus-squared Dirichlet boundary condition. The schemes are combined with a fourth-order Runge-Kutta time-stepping scheme in order to keep the overall method fully explicit. To ensure efficient use of the schemes, a stability analysis is performed to find bounds on the largest usable time step-size as a function of the spatial step-size. The numerical methods are implemented into codes which are run on NVIDIA graphic processing unit (GPU) parallel architectures. The codes running on the GPU are shown to be many times faster than their serial counterparts. The codes are developed with future usability in mind, and therefore are written to interface with MATLAB utilizing custom GPU-enabled C codes with a MEX-compiler interface. Reproducibility of results is achieved by combining the codes into a code package called NLSEmagic which is freely distributed on a dedicated website.

This Thesis is devoted to the investigation of superfluid helium flows due to torsional oscillators. In its first part, flow due to a torsionally oscillating disc suspended on a tungsten filament is studied (building upon the work of A. C. Hollis Hallett from 1952). Measurements of the motion of the torsionally oscillating disc were performed in superfluid helium at temperatures between 1.265 K and 2.157 K at saturated vapour pressure. Time traces of the disc angular deflection were obtained, and critical parameters related to the turbulent flow stability were determined. In laminar flow, scaling of drag forces with the dimensionless Donnelly number was verified. Based on these results, and comparison with the original work, a scenario of the decay of turbulent flow was suggested. The second part of this work is focused on the development and construction of a similar experiment for mK temperatures. A new type of oscillator was designed, a so-called "pillbox", and a series of testing measurements was performed both at room and mK temperatures.

We investigate whether quantum spin rings with nearest-neighbor Heisenberg or Ising exchange interactions can host solitary states. Using complete diagonalization techniques the system is described without classical or semiclassical approximation. In this case definitions used in connection with classical solitons are not applicable, one needs to redefine what solitary objects on a quantum spin system with translational symmetry ought to be. Thus, we start our contribution by defining which quantum states possess solitary character. In addition we discuss useful observables in order to visualize solitary quantum states. Then we demonstrate for various quantum spin rings that solitary quantum states indeed exist, and that they are moving around the spin ring without changing their shape in the course of time.

Das Standart-Modell zur Beschreibung von Observablen magnetischer Moleküle ist das Heisenberg-Modell. In diesem wird der Magnetismus des Superaustausches der Elektronen durch einfache bilineare Spin-Spin-Kopplungen beschrieben. Zur genaueren Approximation experimenteller Ergebnisse können, der jeweiligen Struktur des Moleküls entsprechend, verschiedene Erweiterungen des Heisenberg-Modells verwendet werden. Diese werden, explizit für das 4-Spin-System {Ni4Mo12}, in ihren Auswirkungen auf die Hochtemperatur-Nullfeldsuszeptibilität, die Nullfeldsuszeptibilität und die Hochfeldmagnetisierung betrachtet. Die wesentlichen Erweiterungen sind dabei die Einzelionen-Anisotropie, die Dzyaloshinskii-Moriya-Anisotropie und die allgemeinen Kopplungen zweiter Ordnung. Letztere stellen eine Verallgemeinerung der bekannten biquadratischen Kopplungen dar und werden im Rahmen eines magneto-elastischen Modells hergeleitet. Dabei ergeben sich unterschiedliche Einschränkungen der Kopplungsmatrix zweiter Ordnung für starre und flexible Molekülstrukturen. Speziell für {Ni4Mo12} entsprechen die Ergebnisse numerischer Simulationen von Messwerten einer Strukturänderung im externen Magnetfeld.

Motivated by successes in the image generation domain, this thesis presents a novel Hybrid VQ-VAE (H-VQ-VAE) approach for generating realistic synthetic time series data with categorical features. The primary motivation behind this work is to address the limitations of existing generative models in accurately capturing the underlying structure and patterns of time series data, especially when dealing with categorical features.  Our proposed H-VQ-VAE model builds upon the foundation of the VQ-VAE architecture and consists of two separate VQ-VAEs: the whole VQ-VAE and the sliding VQ-VAE. Both models share a ResNet-based architecture with conv1d layers to effectively capture the temporal structure within the time series data. The whole VQ-VAE focuses on entire sequences of data to learn relationships between categorical and numerical features, while the sliding VQ-VAE exclusively processes numerical features using a sliding window approach. We conducted experiments on multiple datasets to evaluate the performance of our H-VQ-VAE model in comparison with the original VQ-VAE and TimeGAN models. Our evaluation used a train-on-real and test-on-synthetic approach, focusing on metrics such as Mean Absolute Error (MAE) and Explained Variance (EV). The H-VQ-VAE model achieved a 25-50% better MAE for numerical features compared to the VQ-VAE and outperformed TimeGAN by 45-75% on the complex dataset indicating its effectiveness in capturing the underlying structure and patterns of the time series data. In conclusion, the H-VQ-VAE model offers a promising approach for generating realistic synthetic time series data with categorical features, with potential applications in various fields where accurate data generation is crucial.

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