Background and Objectives: I investigated the use of sensitivity analyses in assessing statistical results or analytical approaches in three different statistical issues: (1) accounting for within-subject correlations in analyzing discrete choice data, (2) handling both-armed zero-event studies in meta-analyses for rare event outcomes, and (3) incorporating external information using Bayesian approach to estimate rare-event rates. Methods: Project 1: I empirically compared ten statistical models in analyzing correlated data from a discrete choice survey to elicit patient preference for colorectal cancer screening. Logistic and probit models with random-effects, generalized estimating equations or robust standard errors were applied to binary, multinomial or bivariate outcomes. Project 2: I investigated the impacts of including or excluding both-armed zero-event studies on pooled odds ratios for classical meta-analyses using simulated data. Five commonly used pooling methods: Peto, Mantel-Haenszel fixed/random effects and inverse variance fixed/random effects, were compared in terms of bias and precision. Project 3: I explored the use of Bayesian approach to incorporate external information through priors to verify, enhance or modify the study evidence. Three study scenarios were derived from previous studies to estimate inhibitor rates for hemophilia A patients treated with rAHF-PFM: 1) a single cohort of previously treated patients, 2) individual patient data meta-analysis, and 3) an previously unexplored patient population with limited data. Results and Conclusion: Project 1: When within-subject correlations were substantial, the results from different statistical models were inconsistent. Project 2: Including both-armed zero-event studies in meta-analyses increased biases for pooled odd ratios when true treatment effects existed. Project 3: Through priors, Bayesian approaches effectively incorporated different types of information to strengthen or broaden research evidence. Through this thesis I demonstrated that when analyzing complicated health research data, it was important to use sensitivity analyses to assess the robustness of analysis results or proper choice of statistical models. / Dissertation / Doctor of Philosophy (PhD)

The Swedish Institute of Space Physics (IRF) at Kiruna focuses on research activities in the ionosphere, magnetosphere, and upper atmosphere of the planet as well as the development and production of various sensors and detectors for space research. The test facility includes the IRF SpaceLab which is equipped with multiple testing equipment. One of the testing resources available is the Solar Simulator, which consists of a vacuum chamber equipped with four metal halide lamps that produce a spectrum closely resembling that of the Sun. When any spacecraft payload or instrument is exposed to the Sun and its radiations, the most important factors to consider are the type of radiation, flux, and how the exposed material will react. Thermal designing and solar balance tests are important factors in achieving expected conditions for different missions. By testing and verifying these lamps, this solar simulator can be used not only for IRF missions but also for other institutes and private organizations that can access it. The characterization of four lamps is done in terms of temperature distribution, radiation, and power. According to preliminary experimental measured values obtained from the setup, exposed material, and its properties can be varied and the best suitable coating can be selected that includes α (absorptivity) and ϵ (emissivity) valueconsideration. The thesis is divided into four phases: Designing, Manufacturing, Testing, and Analyzing. Before entering into these phases, the basic knowledge of thermal engineering and thermal simulation is acquired. Thermal modeling and simulations are done in Airbus Defence & Space’s Systema Thermica software tool. The design phase includes designing a frame structure and a 350 x 350 mm screen in Autodesk Inventor software. Manufacturing of the frame structure and the screen was done in the IRF workshop. This screen kept hanging with the support of a frame structure which is mounted on the copper table inside the chamber. The screen is kept in the field of view of each lamp and every lamp is illuminated accordingly. The analysis is done by measuring the temperature of the back side of the screen. Temperature sensors were mounted and clamped mechanically instead of kapton tape to avoid direct contact with the screen. The obtained values are analyzed and compared with the thermally simulated values. Pressure and the temperature of the system were monitored with independent systems throughout the test procedure. This thesis report could operate as a foundation for future examination of the solar simulator’s lamps in order to determine precise efficiency.

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This dissertation builds a model of information exchange, where the information is skills. A two-sided matching market for skills is employed that includes two distinct sides, skilled and unskilled agents, and the matches that connect these agents. The unskilled agents wish to purchase skills from the skilled agents, who each possess one valuable and unique skill. Skilled agents may match with many unskilled agents, while each unskilled agent may match with only one skilled agent. Direct interaction is necessary between the agents to teach and learn the skill. Thus, there must be mutual consent for a match to occur and the skill to be exchanged. In this market for skills, a discrete, simultaneous move game is employed where all agents announce their strategies at once, every skilled agent announcing a price and every unskilled agent announcing the skill she wishes to purchase. First, both Nash equilibria and a correlated equilibrium are determined for an example of this skills market game. Next, comparative statics are employed on this discrete, simultaneous move game through computer simulations. Finally, a continuous, simultaneous move game is studied where all agents announce their strategies at once, every skilled agent announcing a price and every unskilled agent announcing a skill and price pair. For this game, an algorithm is developed that if used by all agents to determine their strategies leads to a strong Nash equilibrium for the game. / Economics

Analogue quantum simulators have proven to be an extremely versatile tool for the study of strongly-correlated condensed matter systems both near and far from equilibrium. An enticing prospect is the quantum simulation of non- Fermi liquids which lack a quasiparticle description and feature prominently in the study of strange metals, fast scrambling of quantum information, as well as holographic quantum matter. Yet, large-scale laboratory realisations of such systems remain outstanding. In this thesis, we present a proposal for the analogue quantum simulation of one such system, the Sachdev–Ye–Kitaev (SYK) model, using cavity quantum electrodynamics (cQED). We discuss recent experimental advances in this pursuit, and perform analysis of this and related models. Through a combination of analytic calculations and numeric simulations, we show how driving a cloud of fermionic atoms trapped in a multi- mode optical cavity, and subjecting it to a spatially disordered AC-Stark shift, can realise an effective model which retrieves the physics of the SYK model, with random all-to-all interactions and fast scrambling. Working towards the SYK model, we present results from a recent proof-of-principle cQED experiment which implemented the disordered light-shift technique to quantum simulate all- to-all interacting spin models with quenched disorder. In this context, we show analytically how disorder-driven localisation can be extracted from spectroscopic probes employed in cQED experiments, despite their lack of spatially resolved information. Further, we numerically investigate the post-quench dynamics of the SYK model, finding a universal, super-exponential equilibration in the disorder-averaged far-from-equilibrium dynamics. These are reproduced analytically through an effective master equation. Our work demonstrates the increasing capabilities of cQED quantum simulators, highlighting how these may be used to study the fascinating physics of holographic quantum matter and other disorder models in the lab.

To follow up on the unexpectedly-good performance of coupled-cluster models with approx- imate inclusion of 3-body clusters [J. Chem. Phys. 151, 064102 (2019)] we performed a more complete assessment of the 3CC method [J. Chem. Phys. 125, 204105 (2006)] for accurate computational thermochemistry in the standard HEAT framework. New spin- integrated implementation of the 3CC method applicable to closed- and open-shell systems utilizes a new automated toolchain for derivation, optimization, and evaluation of operator algebra in many-body electronic structure. We found that with a double-zeta basis set the 3CC correlation energies and their atomization energy contributions are almost always more accurate (with respect to the CCSDTQ reference) than the CCSDT model as well as the standard CCSD(T) model. The mean errors in { 3CC, CCSDT, and CCSD(T) } electronic (per valence electron) and atomization energies were {23, 69, 125} μEh/e and {0.39, 1.92, 2.57} kJ/mol, respectively. The significant and systematic reduction of the error by the 3CC method and its lower cost than CCSDT suggests it as a viable candidate for post-CCSD(T) thermochemistry application. / Doctor of Philosophy / Stepping into the information age, the computing power has rapidly grown over the last half century. Solving chemical problems on computers has improved lives by reducing the cost and time of researching critical technologies. Scientific research is evolving and experimental finding are now supported with a computational model. Doing chemistry on computers requires quantum simulations, which is essentially solving the Schr ̈odinger equation on a computer that simulates a wave function for all the electrons in a system. Different models are built based on how these inter electronic interactions are treated. To predict results with accuracy on par with the experimental findings requires using higher-order wave functions methods.These are computationally expensive and often not practical. The lower-order methods that are easy to implement can be found in all quantum chemistry software packages. On the other hand, the higher-order methods are laborious and error prone to implement manually due to the sheer complexity of theory. Debugging such implementations often requires a lot of effort with the uncertainty in returns. To solve this problem, we implemented a second-quantization toolkit (SeQuant version 2.0) that derives many-body methods, specifically the general-order coupled cluster (CC) model. The CC model is systematically improvable and accurate. One such CC model, the CCSD(T), has been called the gold standard in quantum chemistry. For compactness, these equations are usually derived in their spin-orbital form. The evaluation and storage cost of these methods is reduced up to four-fold by transforming the spin-orbital expressions to a spin-traced form. In this work, the spin-tracing algorithms are described in detail. The general-order coupled cluster approach is used to derive the internally corrected approximate coupled cluster methods. These methods improve the accuracy of a model at a reduced cost. For small molecules, it was observed that the spin-traced evaluation was over three times faster than spin-orbital coupled cluster. To further reduce the cost of calculations, we added explicit correlation to our CC models. These methods improved the quality of our results with a modest increase in the computational cost.

This report, presents an analytical framework for analyzing two-branch diversity systems for a Rayleigh fading channel. In many cases the fading received at both branches (i.e. a two-antenna element system) is correlated because of the proximity of the antenna elements to each other. It is also not uncommon for a diversity system to use antennas with different patterns or polarizations, this usually results in differences in average signal-to-noise ratios at both branches depending on which element is better matched to the signal environment. As will be shown, the performance of a diversity system depends greatly on the envelope correlation, average power imbalance and the combining scheme used on both branches. An analytical expression for the probability density function of the signal-to-noise ratio at the output of a two-branch maximal ratio and selection diversity system is developed in this report. The two branches are assumed to be Rayleigh fading, correlated, as well as of unequal signal-to-noise ratios. Measurements were made in Rayleigh fading channels and compared to the analytical results. The analytical cumulative distribution functions (derived using probability distributions) were found to be within 1 dB of the measured results (statistics obtained from time combining) for both maximal ratio and selection diversity attesting to the validity of the analytic results. Also developed in this report are the exact analytical average probabilities of symbol error for coherent BPSK and coherent QPSK before and after maximal ratio combining for this environment. The diversity gain for selection, maximal ratio, and equal gain combining for the 10% probability level is presented as a function of power imbalance and correlation between branches for a two-branch Rayleigh diversity system / Master of Science

In the rapidly advancing field of quantum technologies, integrated quantum photonics merges quantum mechanics with photonics, promising breakthroughs in communication, sensing, computing, and security. This doctoral thesis investigates the generation of correlated photons via spontaneous four-wave mixing (sFWM) on silicon-based platforms. Through a comparative analysis of various intramodal and intermodal sources, the research focuses on two main areas: applications in sensing within the 2 μm region and the development of sources and other integrated structures in the visible-near infrared region for quantum algorithms, such as variational quantum eigensolver and boson sampler. For sensing, the study enhances quantum ghost spectroscopy to enable efficient gas detection using non-degenerate intermodal silicon sFWM. In the context of quantum simulation, silicon-nitride-based integrated photonic structures were realized to generate and manipulate quantum light within a photonic integrated circuit. Additionally, a proof-of-concept implementation of a two-qubit SWAP test in silicon nitride material showcased significant potential in quantum machine learning.