Background

Results

Conclusions

In order to design more effective catalysts, we deployed X-ray absorption spectroscopy (XAS) to develop structure-activity relationships for supported heterogeneous catalysts. Starting from carefully-designed synthesis, the metal ions are uniformly dispersed on the support. The pre-treatment and other synthetic modifications are strategically chosen to alter the structure and reactivity of the metal sites. Specially, we explored catalytic systems in which the active sites are mononuclear metal complexes grafted on the oxide supports. XAS is essential for probing the local structures of the metal centers, such as electronic properties and coordination geometry. The applications of the catalysts include olefin metathesis, propane dehydrogenation and C-O hydrogenolysis. Monomolybdate sites with relatively uniform first coordination spheres were synthesized by a direct solid-solid reaction between MoO2Cl2 and silica. The resulting Mo(=O)2(OSi)2 sites were characterized and compared to the spectra of several well-defined model molybdate compounds. In extended X-ray absorption fine structure (EXAFS) analysis, the attenuation of the long-range EXAFS features at ca. 3 Å in Mo(=O)2(OSi)2 sites suggests the attachment to the silica surface as molybdasiloxane rings of variable ring size. The partially well-defined Mo(=O)2(OSi)2 sites were treated with a few common activation methods, but failed to catalyze propylene metathesis. Only exposure to olefins at high temperatures (>500 C) leads to promoting propylene metathesis at 23 C and resulting in an active site fraction as high as 36%. However, the co-existence of multiple types of metal sites makes it difficult to identify the active sites. GaiBu3/γ-Al2O3 catalyst promotes propane dehydrogenation at 550 °C, and the Ga species present under reaction conditions were unknown. We used operando XAS to monitor the evolution of Ga K-edge from as-prepared to catalytic conditions. The X-ray absorption near edge structure (XANES) reveals that isobutyl ligands are replaced by oxygen-donor ligands derived from the alumina surface in a single, gradual process, leading to a 3-coordinate mononuclear Ga site at 550 °C. Additional, minor Ga(I) species may form simultaneously. DFT-based simulations elucidate the ligand influence on the Ga K-edge XANES features, such as the white line intensity and edge position. This structural insight sheds light on the correlation between the mononuclear Ga site and the subsequent catalytic activity. The direct synthesis of single-atom Fe catalysts supported on nitrogen-doped carbon gives five-coordinate Fe(III), with four in-plane pyridinic nitrogen donors and one axial hydroxyl ligand. These Fe catalysts exhibit high selectivity, activity, and reusability for C–O bond hydrogenolysis using H2 at temperatures as low as 170 °C. The characterization of the catalyst shows the reduction of Fe(III) to Fe(II) sites with loss of the hydroxyl ligand under reaction conditions. The four-coordinate Fe(II) sites are the active sites for H2-splitting. The interaction between metal sites and the support is critical to promote activity.

Machine learning (ML) is an increasingly popular method to discover the structure and information behind data. In the past years, many efforts have been made on combining ML techniques with quantum mechanics (QM).

Most researches in ML QM predict quantum properties from geometries, trained on the data produced by density functional theory (DFT).

However, using ML to find density functional approximation will be a more fundamental physics problem.

In 2012, the first attempt to apply ML on kinetic energy (KE) functional had achieved chemical accuracy on non-interacting fermions in box, better than any existing approximation.

It is essential to understanding the mechanism of the ML model and how it works. In this dissertation, two detailed technical reports will be presented. First, we explore kernel ridge regression (KRR) on a simple function with only one variable. All randomness are removed and the analysis is rigorous. The relation between underfitting, optimal and overfitting regions with hyperparameters are discussed. We discover that ML a density functional shares similar characteristical behaviors with learning a simple function.

Then, we give a detailed explanation on ML approximation of KE of non-interacting fermions in a one dimensional box . Several important concepts and steps of ML in DFT are explained and tested.

The performance of different kernels and methods of cross-validation are explored. The local principal component analysis (PCA) reconstructs the density manifold and a modified Euler-Lagrange constrained minimization of the ML total energy can give accurate constrained optimal densities.

The development of ML algorithms in DFT includes 1d and 3d. In 1d, we model an interacting quantum system trained on data from density matrix renormalization group calculations.

A set of atomic centered basis are developed to represent density in 1d by PCA and Hirshfeld partitioning.

The Hohenberg-Kohn (HK) universal functional are learned, bypassing the need for a Kohn-Sham scheme.

This approach is applied on a wide range of 1d system, from diatomics to thermodynamic limit.

In 3d, we compare the candidates of density representation. Instead of solving the ground state density via Euler equation, a ML HK map is developed to predict ground state density from external potential. On the 3d H$_2$ and H$_2$O molecules, the energy prediction from the ML density can be 10 times more accurate than direct prediction from external potential.

In machine learning, black-box models that discover underlying relationships in data are more predictive than white-box models, but also more challenging to interpret. The constraint of interpretability for nonlinear black-box models is rooted in the interaction effects between features. Based on modeling needs, a white-box model may be sufficient in some circumstances, but understanding how a black-box model generates predictions is essential out of consideration for accuracy and faithfulness. In this paper, we use three global, model-agnostic interpretability methods (Partial Dependence Plot and Individual Conditional Expectation Plot, Global Surrogate, and Global SHAP through discretization) to explain a diverse class of black-box models and compare their behavior quantitatively and qualitatively. The experiment results demonstrate that the performance of the methods varies when the datasets and black-box models in need of interpretation are different. We prove that the methods provide explanations from several perspectives, and therefore present a strategy that selects the most appropriate interpretability method given a new model on a new dataset.

Since the invention of next-generation RNA sequencing (RNA-seq) technologies, they have become a powerful tool to study the presence and quantity of RNA molecules in biological samples and have revolutionized transcriptomic studies on bulk tissues. Recently, the emerging single-cell RNA sequencing (scRNA-seq) technologies enable the investigation of transcriptomic landscapes at a single-cell resolution, providing a chance to characterize stochastic heterogeneity within a cell population. The analysis of bulk and single-cell RNA-seq data at four different levels (samples, genes, transcripts, and exons) involves multiple statistical and computational questions, some of which remain challenging up to date.

The first part of this dissertation focuses on the statistical challenges in the transcript-level analysis of bulk RNA-seq data. The next-generation RNA-seq technologies have been widely used to assess full-length RNA isoform structure and abundance in a high-throughput manner, enabling us to better understand the alternative splicing process and transcriptional regulation mechanism. However, accurate isoform identification and quantification from RNA-seq data are challenging due to the information loss in sequencing experiments. In Chapter 2, given the fast accumulation of multiple RNA-seq datasets from the same biological condition, we develop a statistical method, MSIQ, to achieve more accurate isoform quantification by integrating multiple RNA-seq samples under a Bayesian framework. The MSIQ method aims to (1) identify a consistent group of samples with homogeneous quality and (2) improve isoform quantification accuracy by jointly modeling multiple RNA-seq samples and allowing for higher weights on the consistent group. We show that MSIQ provides a consistent estimator of isoform abundance, and we demonstrate the accuracy of MSIQ compared with alternative methods through both simulation and real data studies. In Chapter 3, we introduce a novel method, AIDE, the first approach that directly controls false isoform discoveries by implementing the statistical model selection principle. Solving the isoform discovery problem in a stepwise manner, AIDE prioritizes the annotated isoforms and precisely identifies novel isoforms whose addition significantly improves the explanation of observed RNA-seq reads. Our results demonstrate that AIDE has the highest precision compared to the state-of-the-art methods, and it is able to identify isoforms with biological functions in pathological conditions.

The second part of this dissertation discusses two statistical methods to improve scRNA-seq data analysis, which is complicated by the excess missing values, the so-called dropouts due to low amounts of mRNA sequenced within individual cells. In Chapter 5, we introduce scImpute, a statistical method to accurately and robustly impute the dropouts in scRNA-seq data. The scImpute method automatically identifies likely dropouts, and only performs imputation on these values by borrowing information across similar cells. Evaluation based on both simulated and real scRNA-seq data suggests that scImpute is an effective tool to recover transcriptome dynamics masked by dropouts, enhance the clustering of cell subpopulations, and improve the accuracy of differential expression analysis. In Chapter 6, we propose a flexible and robust simulator, scDesign, to optimize the choices of sequencing depth and cell number in designing scRNA-seq experiments, so as to balance the exploration of the depth and breadth of transcriptome information. It is the first statistical framework for researchers to quantitatively assess practical scRNA-seq experimental design in the context of differential gene expression analysis. In addition to experimental design, scDesign also assists computational method development by generating high-quality synthetic scRNA-seq datasets under customized experimental settings.

In item response theory (IRT), the underlying latent variables are typically assumed to be normally distributed. If the assumption of normality is violated, the item and person parameter estimates can become biased. Therefore, it is necessary in practical data analysis situations to examine the adequacy of this assumption in an effective manner. There is a recent surge of interest in limited-information overall goodness-of-fit test statistics for IRT models (see e.g., Cai, Maydeu-Olivares, Coffman, & Thissen, 2006; Joe & Maydeu-Olivares, 2010; Cai & Hansen, 2013), but their appropriateness for diagnosing latent variable distributional fit has not been studied.

The approach undertaken in this research is to use summed score likelihood based indices. The idea itself is not new (see e.g., Ferrando & Lorenzo-Seva, 2001; Hambleton & Traub, 1973; Lord, 1953; Ross, 1966; Sinharay, Johnson, & Stern, 2006; Thissen & Wainer, 2001), but this study recasts the problem using the framework of limited-information goodness of fit testing. The summed score based indices can be viewed as a particular form of reduction of the full underlying multinomial that are potentially sensitive to the latent variable distributional misspecifications.

Results from a pilot study (Li & Cai, 2012) show that summed score likelihood based indices enjoy high statistical power for detecting latent variable distributional assumption violations, and are not sensitive (correctly) to other forms of model misspecification such as unmodeled multidimensionality. Meanwhile, the limited-information overall fit statistic M2 (Maydeu-Olivares & Joe, 2005) has relatively low power against latent variable non-normality. However, technically the statistical indices proposed by Li and Cai (2012) don't follow an exactly chi-squared distribution. They proposed a heuristic degrees of freedom adjustment, but more rigorous justifications could be developed along the lines of Sattora-Bentler type moment adjustment popular in structural equation modeling (Satorra & Bentler, 1994). In IRT, the moment adjustment approaches have been used by Cai et al. (2006) and Maydeu-Olivares (2001).

The major methodological contributions of my dissertation come from simulation studies that examine the calibration and power of the moment adjusted test statistics across various conditions: number of items, sample size, item type, generating latent variable distribution, and the values of generating item parameters. The performance of these fit statistics are also compared with M2. Simulation study results show that the proposed moment-adjusted statistics improve upon the unadjusted statistics in the null and alternative conditions, especially when generating item parameters are dispersed. Finally, performance of the indices is illustrated with empirical data from educational and psychological assessment development projects.