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.

Conventional correlation methods suffer from the slow convergence of electron correlation energies with respect to the size of orbital expansions. This problem is due to the fact that orbital products alone cannot describe the behavior of the exact wave function at short inter-electronic distances. Explicitly correlated methods overcome this basis set problem by including the inter-electronic distances (rij) explicitly in wave function expansions. Here, the origin of the basis set problem of conventional wave function methods is reviewed, and a short history of explicitly correlated methods is presented. The F12 methods are the focus herein, as they are the most practical explicitly correlated methods to date. Moreover, some of the key developments in modern F12 technology, which have significantly improved the efficiency and accuracy of these methods, are also reviewed. In this work, the extension of the perturbative coupled-cluster F12 method, CCSD(T)F12, developed in our group for the treatment of high-spin open-shell molecules (J. Zhang and E. F. Valeev, J. Chem. Theory Comput., 2012, 8, 3175.), is also documented. Its performance is assessed for accurate prediction of chemical reactivity. The reference data include reaction barrier heights, electronic reaction energies, atomization energies, and enthalpies of formation from the following sources: (1) the DBH24/08 database of 22 reaction barriers (Truhlar et al., J. Chem. Theory Comput., 2007, 3, 569.), (2) the HJO12 set of isogyric reaction energies (Helgaker et al., Modern Electronic Structure Theory, Wiley, Chichester, first ed., 2000.), and (3) the HEAT set of atomization energies and heats of formation (Stanton et al., J. Chem. Phys., 2004, 121, 11599.). Two types of analyses were performed, which target the two distinct uses of explicitly correlated CCSD(T) models: as a replacement for the basis-set-extrapolated CCSD(T) in highly accurate composite methods like HEAT and as a distinct model chemistry for standalone applications. Hence, (1) the basis set error of each component of the CCSD(T)F12 contribution to the chemical energy difference in question and (2) the total error of the CCSD(T)F12 model chemistry relative to the benchmark values are analyzed in detail. Two basis set families were utilized in the calculations: the standard aug-cc-p(C)VXZ (X = D, T, Q) basis sets for the conventional correlation methods and the cc-p(C)VXZ-F12 (X = D, T, Q) basis sets of Peterson and co-workers that are specifically designed for explicitly correlated methods. The conclusion is that the performance of the two families for CCSD correlation contributions (which are the only components affected by the explicitly correlated terms in our formulation) are nearly identical with triple- and quadruple-ζ quality basis sets, with some differences at the double-ζ level. Chemical accuracy (~4.18 kJ/mol) for reaction barrier heights, electronic reaction energies, atomization energies, and enthalpies of formation is attained, on average, with the aug-cc-pVDZ, aug-cc-pVTZ, cc- pCVTZ-F12/aug-cc-pCVTZ, and cc-pCVDZ-F12 basis sets, respectively, at the CCSD(T)F12 level of theory. The corresponding mean unsigned errors are 1.72 kJ/ mol, 1.5 kJ/mol, ~ 2 kJ/mol, and 2.17 kJ/mol, and the corresponding maximum unsigned errors are 4.44 kJ/mol, 3.6 kJ/mol, ~ 5 kJ/mol, and 5.75 kJ/mol. In addition to accurate energy calculations, our studies were extended to the computation of molecular properties with the MP2-F12 method, and its performance was assessed for prediction of the electric dipole and quadrupole moments of the BH, CO, H2O, and HF molecules (J. Zhang and E. F. Valeev, in preparation for submission). First, various MP2- F12 contributions to the electric dipole and quadrupole moments were analyzed. It was found that the unrelaxed one-electron density contribution is much larger than the orbital response contribution in the CABS singles correction, while both contributions are important in the MP2 correlation contribution. In contrast, the majority of the F12 correction originates from orbital response effects. In the calculations, the two basis set families, the aug-cc-pVXZ (X = D, T, Q) and cc-pVXZ-F12 (X = D, T, Q) basis sets, were also employed. The two basis set series show noticeably different performances at the double-ζ level, though the difference is smaller at triple- and quadruple-ζ levels. In general, the F12 calculations with the aug-cc- pVXZ series give better results than those with the cc-pVXZ-F12 family. In addition, the contribution of the coupling from the MP2 and F12 corrections was investigated. Although the computational cost of the F12 calculations can be significantly reduced by neglecting the coupling terms, this does increase the errors in most cases. With the MP2-F12C/aug-cc-pVDZ calculations, dipole moments close to the basis set limits can be obtained; the errors are around 0.001 a.u. For quadrupole moments, the MP2-F12C/aug-cc-pVTZ calculations can accurately approximate the MP2 basis set limits (within 0.001 a.u.). / Ph. D.

Accurate correlated electronic structure methods involve a significant amount of computations and can be only employed to small molecular systems. For example, the coupled-cluster singles, doubles, and perturbative triples model (CCSD(T)), which is known as the ``gold standard" of quantum chemistry for its accuracy, usually can treat molecules with 20-30 atoms. To extend the reach of accurate correlated electronic structure methods to larger molecular systems, we work towards two directions: parallel computing and reduced-cost/scaling approaches. Parallel computing can utilize more computational resources to handle systems that demand more substantial computational efforts. Reduced-cost/scaling approaches, which introduce approximations to the existing electronic structure methods, can significantly reduce the amount of computation and storage requirements. In this work, we introduce a new distributed-memory massively parallel implementation of standard and explicitly correlated (F12) coupled-cluster singles and doubles (CCSD) with canonical bigO{N^6} computational complexity ( C. Peng, J. A. Calvin, F. Pavov{s}evi'c, J. Zhang, and E. F. Valeev, textit{J. Phys. Chem. A} 2016, textbf{120}, 10231.), based on the TiledArray tensor framework. Excellent strong scaling is demonstrated on a multi-core shared-memory computer, a commodity distributed-memory computer, and a national-scale supercomputer. We also present a distributed-memory implementation of the density-fitting (DF) based CCSD(T) method. (C. Peng, J. A. Calvin, and E. F. Valeev, textit{in preparation for submission}) An improved parallel DF-CCSD is presented utilizing lazy evaluation for tensors with more than two unoccupied indices, which makes the DF-CCSD storage requirements always smaller than those of the non-iterative triples correction (T). Excellent strong scaling is observed on both shared-memory and distributed-memory computers equipped with conventional Intel Xeon processors and the Intel Xeon Phi (Knights Landing) processors. With the new implementation, the CCSD(T) energies can be evaluated for systems containing 200 electrons and 1000 basis functions in a few days using a small size commodity cluster, with even more massive computations possible on leadership-class computing resources. The inclusion of F12 correction to the CCSD(T) method makes it converge to basis set limit much more rapidly. The large-scale parallel explicitly correlated coupled-cluster program makes the accurate estimation of the coupled-cluster basis set limit for molecules with 20 or more atoms a routine. Thus, it can be used rigorously to test the emerging reduced-scaling coupled-cluster approaches. Moreover, we extend the pair natural orbital (PNO) approach to excited states through the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) method. (C. Peng, M. C. Clement, and E. F. Valeev, textit{submitted}) We simulate the PNO-EOM-CCSD method using an existing massively parallel canonical EOM-CCSD program. We propose the use of state-averaged PNOs, which are generated from the average of the pair density of excited states, to span the PNO space of all the excited states. The doubles amplitudes in the CIS(D) method are used to compute the state-averaged pair density of excited states. The issue of incorrect states in the state-averaged pair density, caused by an energy reordering of excited states between the CIS(D) and EOM-CCSD, is resolved by simply computing more states than desired. We find that with a truncation threshold of $10^{-7}$, the truncation error for the excitation energy is already below 0.02 eV for the systems tested, while the average number of PNOs is reduced to 50-70 per pair. The accuracy of the PNO-EOM-CCSD method on local, Rydberg and charge transfer states is also investigated. / Ph. D.