Over the past century, China has undertaken the strenuous work of developing its own civil code to regulate civil matters. The codification project began in the early 20th century and culminated in 1930 with the enactment of China’s first Civil Code. In the meantime, the philosophy, culture, and mentality in the courtroom also changed, influenced by the new civil codification and professional training of legal professionals. These changes were not limited to a specific temporal or spatial context but denoted a transformation of the culture of judicial practice in China that accompanied the modernization of law. Drawing on cases from the Beijing High Court (1912–1928), this dissertation examines how appellate judges in Beijing reviewed decisions from lower courts in marriage-related cases and how judges reasoned through and resolved cases by adapting the newly introduced civil law tradition to traditional Chinese legal culture. Given that the legitimacy of normativity originated from different sources, this dissertation argues that there emerged an meso ground between potential legal bases and judicial decisions, where an array of legal bases was collated, debated, and reconciled in alignment with societal norms and traditions to develop compelling judgments. In some particular cases, this meso ground was fluid, embracing both domestic and foreign legal concepts. Leveraging the flexibility of translation, this meso ground also worked to integrate the historical legacy of imperial Chinese law and the fresh realities, ambitions, and legal trajectory of China during the early 20th century. This methodology and philosophy regarding the organization of law in China came to be called as multisourcing and has endured to the present day.

Dielectric elastomers (DEs) are a new type of smart materials showing promising functionalities as energy harvesting materials as well as actuating materials for potential applications such as artificial muscles, implanted medical devices, robotics, loud speakers, micro-electro-mechanical systems (MEMS), tunable optics, transducers, sensors, and even generators due to their high electromechanical efficiency, stability, lightweight, low cost, and easy processing. Despite the advantages of DEs, technical challenges must be resolved for wider applications. A high electric field of at least 10-30 V/um is required for the actuation of DEs, which limits the practical applications especially in biomedical fields. We tackle this problem by introducing the multiwalled carbon nanotubes (MWNTs) in DEs to enhance their relative permittivity and to generate their high electromechanical responses with lower applied field level. This work presents the dielectric, mechanical and electromechanical properties of DEs filled with MWNTs. The micromechanics-based finite element models are employed to describe the dielectric, and mechanical behavior of the MWNT-filled DE nanocomposites. A sufficient number of models are computed to reach the acceptable prediction of the dielectric and mechanical responses. In addition, experimental results are analyzed along with simulation results. Finally, laser Doppler vibrometer is utilized to directly detect the enhancement of the actuation strains of DE nanocomposites filled with MWNTs. All the results demonstrate the effective improvement in the electromechanical properties of DE nanocomposites filled with MWNTs under the applied electric fields.

Many algorithms in Machine Learning have demonstrated powerful empirical performance in terms of prediction accuracy and ability to extract knowledge from data. Inspired by the empirical success, researchers study the behavior of those algorithms under theoretical models. Two challenges must be addressed when one {tries} to understand those algorithms from a theoretical perspective. First, a sound theoretical model should be considered. A good model should reflect key properties of the real data. If the models do not capture important aspects of the real data, the observations and/or conclusions made on those theoretical models {may not be relevant} to practice. Thus, theoretical models that reflect certain properties of real data are required so that the insights obtained from those models are convincing to practitioners. Second, many of these algorithms are hard to analyze via traditional techniques. Therefore, novel techniques are required to analyze those algorithms under new theoretical models. In this thesis, we analyze two problems under novel real-data inspired theoretical models: $\ell_1$-minimization for dictionary learning and seeking important features and feature interactions from {Random Forest} (RF). Both analyses give unique insights into the problem by studying a novel data generative model. For dictionary learning, we propose two novel theoretical models: exact sparse model and Bernoulli-type models. Unlike most previous {analyses} that assume the data is {generated from} Gaussian distributions with sparsity constraints, these new models can capture non-Gaussian data distributions and allow us to analyze the algorithms under novel data properties such as non-negativity and heavy-tail. We show that $\ell_1$-minimization model in Dictionary Learning does not satisfy the classic global identifiability condition under the new model. However, the reference dictionary still enjoys some global property across all the feasible dictionaries. Our theoretical analysis leads to a novel algorithm called Dictionary Learning Block Coordinate Descent (DL-BCD). For RF, we start off with analyzing the feature importance bias for noisy features when using Mean Decrease Impurity (MDI). Then, we study the feature interaction recovery problem and analyzed the data-inspired Local-Spiky Sparse (LSS) model without Lipschitz assumptions that are often present in the previous literature. We show that the depth-weighted-prevalence of a true feature interaction in the decision paths of trees does not depend on the model coefficients but only on the size of the interaction. The theoretical analysis leads to a novel feature ranking method called LSSrank. We examine the performance of LSSrank on simulated data and it has high probability to rank true interactions at the top under the LSS model.

Deep neural networks usually have many hyperparameters that need to be tuned. Modern material design problems usually require material scientists to sequentially select processing parameters and conduct experiments to observe material performances. To save privacy cost, the learning system needs to carefully choose queries to answer under the differential privacy framework. To train a robot under video guidance, engineers need to carefully choose video samples for training. However, in all cases, people cannot observe performances of unselected actions and the experimental cost can be huge. These two challenges hinder efficient neural network training, new material design, privacy protection, and robot training and call for actions. In this thesis, I present my research on optimization, bandits, and active learning under the adaptive sequential decision making framework. My algorithms are able to solve black box function optimization without the curse of dimensionality, achieve no regret under the function class misspecification, reduce privacy cost under the differential privacy framework, and significantly reduce video sample complexity for robot training. All of them come with theoretical or empirical analysis.

With increasing ethical and legal concerns on privacy in the era of big data, differential privacy (DP) has emerged as the de facto gold standard to disguise membership of individuals with quantiiable privacy guarantee. In DP, the theoretical privacy guarantee directly corresponds to the amount of noise and randomness that must be introduced into a DP mechanism. Therefore, to employ DP algorithms in the real world, it is crucial to develop a tight characterization of privacy analysis. This thesis aims to bridge the gap between theory and DP deployment by refining the constants in privacy guarantees. In the first part of the thesis, we focus on modern privacy accountings, which characterize privacy degradation through fine-grained mechanism-specific analysis, driving much of the recent success in DP deployments. We enhance these modern privacy accountings by generalizing the PLD formalism to handle adaptive composition and amplification by sampling, two foundamental components in the design of DP algorithms. Additionally, we derive nearly optimal bounds for characterizing privacy amplification by sampling in the R´enyi DP framework, which directly translate into practical enhancements in private deep learning. In the second part of the thesis, we address the mathematical slack in privacy analysis by incorporating data-adaptive analysis, enabling less noise injection when the input dataset is deemed “nice”.

Offline reinforcement learning, a field dedicated to optimizing sequential decision-making strategies using historical data, has found widespread application in real-world scenarios. Recent years have witnessed a surge in research focusing on establishing the statistical foundations for offline reinforcement learning, with many studies achieving near-optimal worst-case performance bounds. However, empirical results often outperform these non-adaptive bounds significantly. A comprehensive understanding of which decision processes and behavior policies are inherently more amenable or challenging for offline RL remains elusive. To address this critical challenge, the first part of this thesis delves into instance-dependent offline learning within tabular Markov Decision Processes. We introduce the Adaptive Pessimistic Value Iteration algorithm, which achieves an instance-dependent guarantee and is also near optimal. This result subsumes a wide spectrum of previous worst-case optimal results, leading to the first instance-dependent guarantee that characterizes the hardness for offline RL.

In the Second chapter of the thesis, we extend our study for tabular reinforcement learning to the function approximation regime. Specifically, within the context of linear function approximation, we present the variance-aware pessimistic value iteration (VAPVI) algorithm, which quantifies the uncertainty of training examples through conditional variance reweighing. VAPVI enhances offline learning bounds compared to the best-known existing results. Crucially, our learning bounds are expressed in terms of system-related quantities, offering natural instance-dependent characterizations that previous studies lacked.

Furthermore, State-Of-The-Art algorithms usually leverage powerful function approximators (e.g. neural networks) to alleviate the sample complexity hurdle for better empirical performances. In the third chapter, we broaden our focus to function approximation without imposing specific structural constraints on the function class, except for differentiability. This class naturally encompasses a wide range of models with nonlinear and nonconvex structures. Importantly, we demonstrate the provable efficiency of offline RL with differentiable function approximation through an analysis of the pessimistic fitted Q-learning (PFQL) algorithm. Our findings provide the theoretical underpinnings for understanding various practical heuristics relying on Fitted Q-Iteration-style design.

We conclude the thesis by summarizing our work and mentioning other exciting research projects.

We present the runtime comparison of the two versions of Super LU_DIST, using up to 128 processors of the IBM SP at NERSC. One version provides the global input interface, and another provides the distributed input interface. The comparison includes the total runtime of the solver with both 32-bit and 64-bit addressing modes, the time breakdown for different phases of the solver. We also present an in-depth comparison off our sparse matrix-vector multiplication methods in the context of iterative refinement. Finally, we describe our Fortran 90 interface that enhances the usability of the software.

Making decisions in real-time by learning patterns in an online data-stream is an important problem in modern machine learning (ML). Applications that fall under this umbrella include domain adaptation, change-point detection, portfolio-optimization, optimally pricing airline tickets based on changing market features etc. The features of the environment where an ML model is deployed change from time to time. Designing decision-making algorithms that can quickly adapt to these environmental changes on-the-fly is a topic of great significance.

In this thesis, we will design and analyse information-theoretically optimal algorithms for online decision-making under non-stationarities. The presentation will also encompass the utilization of these algorithms across a wide spectrum of applications, spanning time series forecasting, dynamic pricing, non-parametric regression, LQR control and unsupervised domain adaptation.

A main challenge in the theoretical analysis of the algorithms is to exploit the curved geometry of loss functions while deriving fast dynamic regret rates. This is attained by connecting ideas from the domains of locally adaptive non-parametric regression and strongly adaptive online learning. These fields have been conventionally studied separately by researchers. In this thesis we provide new tools to bridge these two domains. A byproduct of this fusion are novel results that do not require observation models with stringent stochastic assumptions for non-parametric regression and online convex optimization. Further, the developed algorithms are highly adaptive and do not require prior knowledge about the degree of non-stationarity in the environment. Our hope is that this thesis will inspire new collaborations between researchers from the communities of online learning and non-parametric regression.