Directed Acyclic Graphs (DAGs) are a powerful tool to model the network of dependencies among variables. They provide a basis for causal discovery, and have been widely used in many fields, especially biology. Unfortunately, structure learning is quite non-trivial for DAG. One major difficulty is that some DAGs are unidentifiable with observational data only, and undirected edges cannot be resolved to directed edges.

The opportunity to apply interventions motivates interest in the smaller interventional Markov equivalence class. In this dissertation, we discuss how to modify the classic PC algorithm for causal discovery so that it can be used safely on interventional data. We introduce invariance relations on conditional distributions with different intervention targets that provide a powerful rule for edge orientation. There are several advantages of this rule: first, it does not require the Gaussian distribution assumption, instead a general structural equation model (SEM) of DAG is sufficient; second, it works for both (structural) intervention and soft intervention. Finally, we can merge some data blocks with different interventions for edge orientation.

A new constraint-based method is proposed to recover the interventional essential graph from the CPDAG (or called as observational essential graph) based on the invariance rule. We also establish consistency guarantees for both an interventional PC and an edge orientation algorithm under a sparse high-dimensional setting. Such high-dimensional consistency results are rarely seen in this area. It is also worthwhile to emphasize that the constraints on the family of interventions throughout this dissertation are mild. Finally, simulations are used to show the effectiveness of our method.

The focus of this thesis is on the multi-agent rendezvous problem where the rendezvous location has the total squared shortest distance to certain regions. Three algorithms

are experimentally implemented under an undirected communication topology. Simulation plots and experimental results are demonstrated on a multi-robot platform to validate the proposed algorithms. First, an implementation of the distributed subgradient shortest-distance rendezvous algorithm is implemented. Second, an alternative distributed shortest-distance rendezvous algorithm which introduces a kind of diminishing step sizes is validated. Third, an algorithm with employment of two internal states of the dynamic averaging estimator is implemented. This thesis illustrates the three algorithms by presenting simulation plots in Matlab, robots’ moving trajectories in the multi-robot platform, and plots of the shortest distance performance function.

Millimeter-Wave (mmWave) Integrated Circuit (IC) design has become a promising research topic since last decade. Millimeter-Wave signals (30GHz to 300GHz) benefit from ultra-high bandwidth and unique physical attributes. With the portability brought by IC techniques, mm-wave chips have enabled applications such as ultra-high-speed (5G/6G) communications, mobile satellite communications, Internet-of-Things (IoT) sensors, ultra-high-resolution radar and various kinds of dieletric, biomedical and chemical sensors. However, with stringent power budget of portable devices and the power-hungry attribute of mmWave circuits, low-power and low-noise on-chip mmWave signal generation and radar design are faced with great challenges.In the first part of this dissertation, a new mmWave frequency synthesizer structure is proposed. Based on Sub-Sampling Phase-Locked Loop (SSPLL) technique, the generated signal achieves low in-band phase-noise. With the proposed dividerless frequency acquisition technique based on a Sub-Sampling Lock Detector (SSLD) and on-chip intermediate-frequency PLL (IF-PLL), the SSPLL can automatically detect its lock status and lock to the correct target frequency without using power-hungry mmWave Injection-Locking Frequency Dividers (ILFD). To verify the proposed system, a prototype 40.5GHz SSPLL chip has been taped out in 65nm CMOS. Due to the relatively low-frequency operation and moderate noise requirement of IF-PLL, as well as the low-power SSLD, the proposed system achieves low power consumption and jitter simultaneously. The measured results show an 8.8mW power consumption and 228fs RMS jitter with in-band and out-band phase noise of -96.6dBc/Hz at 1MHz offset and -106.9dBc/Hz at 10MHz offset, respectively. Another critical issue of charge pump (CP) current mismatch and its exclusive effects on SSPLL are presented in this dissertation. Transistor’s channel-length-modulation (CLM) effect induces SSPLL loop gain distortion and decreases VCO control voltage (Vctrl) locking range (LR). A feedback based compensation method, which is the first-published solution to SSPLL CP mismatch, is then proposed. In a prototype mmWave SSPLL with the proposed compensated CP, the CLM effect is cancelled and Vctrl LR is extended from 0.50V to 0.75V under a 1V supply, without degrading SSPLL noise performance much. As a result of the more efficient use of Vctrl range, VCO capacitor bank setup number is reduced from 10 to 7 to cover the same 10% total tuning range. The compensation circuitry consumes only 0.36mW power. The prototype 40.5GHz SSPLL consumes only 9.5mW power with 192fs RMS jitter. Radar sensors with ultra-high range resolutions have great potential in non-contact sensing of human vital signs, biomedical signals, material thickness and mechanical vibration, and in imaging. With short wavelengths for high resolution and relatively simple structure, mmWave Doppler radar has become a competitive candidate in various displacement-sensing applications. However, issues like detection nulls, nonlinear gain and quadrature signal paths mismatch limit the performance of mmWave Doppler radar. In the last part of this dissertation, a novel system structure of Doppler radar front end is proposed utilizing the intrinsic low added in-band noise feature of SSPLL and a proposed quadrature-less demodulation method. A prototype 110mW 39GHz Doppler radar front end in 65nm CMOS for displacement and vibration sensing is presented. Sub-sampling PLLs (SSPLL) generate single-tone radiated signal. A proposed phase demodulator (PDM) uses coherent IF demodulation to convert displacement to a DC/baseband signal with constant gain. Detection nulls in conventional Doppler radars are eliminated without using quadrature demodulation. The prototype radar achieves 4µm static and 77nm vibrational (at 10KHz) range resolutions.

The general concept of developing gateable host-guest systems is a powerful one with many potential applications such as drug delivery and sensing. In this work, we designed and synthesized a reversible photoswitchable hemicarcerand. This hemicarcerand has an anthracene unit as the photoactive gating element and the reversible opening and closing of the "gate" of the host is well controlled photochemically. Various spectroscopic methods such as 1H NMR and fluorescence demonstrate that, hemicarcerand host-guest complexes are stable to decomplexation at ambient temperatures in the photodimer structure, while release of guests such as 1,4-dimethoxybenzene is achieved by opening the gate by photochemically generating the anthracene monomers.

The second part of this dissertation involves the use of computational chemistry to understand the origins of stereoselectivity in synthetically useful reactions. In collaboration with Prof Wicha's group in Poland, alkylation reactions of azulenone precursors in the guanacastepene A synthesis were studied and steric effects were determined as the origins of different stereoselectivities observed experimentally. Next, in collaboration with Prof Jung's group in UCLA, an unusual conformational effect on reactivities in a cyclic non-aldol aldol rearrangement was explained using theoretical models. In collaboration with Prof Overman, the stereoselectivities of the dihydroxylations of cis-bicyclo[3.3.0]octene intermediates for total synthesis of chromodorolide A were investigated and torsional effects were identified as the control elements here. Other related examples from the literatures were also studied and it was found that the stereoselectivity was greatly affected by the rigidity or flexibility of conformations of reactants. Finally, in collaboration with Prof Antilla, a theoretical study of chiral Brønsted acid-catalyzed allylboration and propargylation reactions was performed. The general reaction mechanisms involving two different models were investigated, and the steric repulsions between the bulky 3,3'-substituents in the catalyst and the substrates were determined to be responsible for the enantioselectivities.

The advent of Single-cell transcriptome sequencing (scRNA-Seq) has revolutionized our ability to explore the intricate landscape of cellular diversity within complex biological systems. Initially focused on cataloging cell subtypes and discerning gene expression disparities across cell types, scRNA-Seq has evolved to address broader inquiries, particularly in the realm of human health. While past efforts concentrated on analyzing numerous cells from a few samples, there’s now a growing interest in understanding inter-sample heterogeneity and its implications for phenotypic outcomes, notably in cancer and inflammatory diseases. However, existing bioinformatic methodologies inadequately address population-level analyses, with limited consideration for inter-sample variation. The dissertation introduces a novel framework termed GloScope Representation, which is introduced in the first chapter in detail, for representing the entire single-cell profile of a sample. In the second chapter, We applied GloScope across scRNA-Seq datasets spanning diverse study designs, with sample sizes ranging from 12 to over 300. Through illustrative examples, we showcase how GloScope empowers researchers to undertake pivotal bioinformatic tasks at the sample level, with a primary focus on visualization and quality control assessment. In Chapter 3, we demonstrate GloScope’s efficacy in evaluating and quantifying batch effects, as well as comparing various batch correction methods’ performance in the patient level analysis of scRNASeq data. Furthermore, to assess GloScope ’s advantages and effectiveness in detecting different classes of single-cell differences arising from variations in sample phenotypes, we compared GloScope to existing visualization tool and other sample level analysis tool in Chapter 4. We also developed a simulation pipeline for generating single-cell count data. We utilize this simulation framework to conduct quantitative evaluations of GloScope through a series of simulated experiments.