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Transcriptional regulation in human cells is a complex process that requires the collaboration of diverse genomic elements and chemicals. To understand the mechanisms, projects including the Encyclopedia of DNA Elements (ENCODE), Roadmap Epigenomics, and 4D Nucleome (4DN) have generated thousands of genomic and epigenomic datasets. These datasets annotated functional elements for the human genome (e.g., enhancers and promoters), summarized experimental results for epigenomic features (e.g., protein binding locations), and linked different modalities with statistical models (e.g., GWAS and eQTLs). From the available data, it has become apparent that the human genome should not be over-simplified as a 1-D linear sequence. Long-range dependencies on DNA sequences play a vital role in human transcriptional regulation. For example, enhancers, the primary units of gene expression regulation, often reside hundreds of kilobases away from their target genes. Enhancers engage in physical interactions with target genes across vast genomic distances to activate them. Therefore, interpreting the human genome requires a more advanced data structure capable of capturing long-distance and complicated relationships. This dissertation discusses how to decipher the human genome as a graph. Graphs, composed of nodes (or vertices) and edges, provide a powerful framework for modeling relationships. Graphs have been proven effective in representing relationships in diverse real-world scenarios, such as social networks, transportation systems, and communication networks. In the subsequent chapters, the representations of the human genome as a graph will be introduced and explored. Chapter 2 introduces the application of chromosome conformation capture (3C) technology, which unveils physical interactions among genomic regions. Analyzing the large-scale contact maps generated by 3C technology is instrumental in uncovering the long-range dependencies of genomic entities and understanding transcriptional regulation. Therefore, we developed computational tools including scHiCTools and Quagga to extract structural features from these maps. In Chapter 3, we addressed the importance of high-resolution and high-quality chromatin contact maps. Therefore, we developed a computational model, CAESAR, to connect epigenomics and high-resolution chromatin structure. CAESAR successfully imputes an unprecedented number of high-resolution human chromatin contact maps, which allows users to easily navigate these fine-scale chromatin structures and the corresponding regulatory mechanisms. Beyond 3D interactions, numerous data consortia and databases unveil the characteristics of genomic entities and their relationships. Despite the invaluable insights provided by these consortia, the separately stored tabular data remain in a 1D sequential framework, posing inconveniences for genomic research and scientific discoveries. To address this challenge, we introduce the Genomic Knowledgebase (GenomicKB) in Chapter 4. GenomicKB is a knowledge graph that seamlessly integrates datasets and annotations related to the human genome into a knowledge graph. Through a graph-based interpretation of the human genome, we anticipate that genomic research will increasingly become data-driven. GenomicKB aims to provide high-quality and integrated data for large-scale machine learning methods, thereby facilitating scientific discoveries.

A helical structure is a collection of molecules at positions given by the orbit of a helical group acting on the position vectors of the atoms of a single molecule. In this thesis, we systematically study phase transformations from one helical structure to another and search for potential applications. Motivated in part by recent work that relates the presence of compatible interfaces with properties such as the hysteresis and reversibility of a phase transformation, we give necessary and sufficient conditions on the structural parameters of two helical phases such that they are compatible. We show that, locally, four types of compatible interfaces are possible: vertical, horizontal, helical and elliptical. Furthermore, we discuss more complex microstructures in transforming helical structures that mix different types of these interfaces. Similar to crystal case, we conjecture that compatible helical transformations with low hysteresis and fatigue resistance would exhibit an unusual shape memory effect involving both twist and extension. The example we give for the application side is the phase-transforming helical Miura origami (HMO). An HMO is the origami structure generated by applying a helical group on a unit cell. The unit cell here is a partially folded four-fold Miura parallelogram. Here we demonstrate the methodology to construct a closed HMO and study its phase transformation properties. To do this, firstly, we conduct a rigorous analysis of the kinematics of the unit cell. We show that, by choosing discrete Abelian group generators and satisfying special discrete conditions, the HMO is generated to close itself at some isolated folding angle, which also means the structure is rigid. Furthermore, inspired by compatible interfaces we have in helical structures, we show that compatible horizontal and helical interfaces occur between two variants − the two different ways of folding for the same unit cell. By transforming one variant to the other, finally, we achieve overall twist and extension actuation, which can be used to develop novel actuators and artificial muscles.

Beaches are always the ideal ocean vacation destination to relax, and most people in tropical regions like to spend time on the beach. Hawaii has some of the best beaches in the world, attracting great numbers of visitors as well as local residents. The environmental quality of beaches, including beach sand and beach water, are essential to the health and safety of beach users and residents. However, in recent years, bacteriological contamination of beaches has steadily increased nationwide, and public concerns on the health and safety of beach usage have raised considerablely. A survey of water quality at U.S. beaches by National Research Defense Council (NRDC) indicated that in 2009 beach water pollutions caused beach closings and advisories to reach their sixth-highest level in 20 years, exceeding 20,000 for the fourth consecutive year (1). In Hawaii, a different trend has been observed. In the past five years, the highest number of total closing/advisory days was in 2006 (6,507 days) while a significantly reduced number of closing/advisory days (2,352 days) were reported in 2009, which are likely due to variations in heavy rainfall frequencies, as more than 99% of the closing/advisory days were issued due to anticipated rainfall events (1). One primary concern of beach water pollution is the increased health risks to beach users. Polluted beach sand and water by untreated sewage and human and animal wastes may contain harmful bacteria and pathogens that post direct health risk to beach users especially children. Diseases caused by waterborne pathogen include gastroenteritis; hepatitis A; ear, nose, and throat infections; severe respiratory ailments; diarrhea; and rashes. In order to reduce illnesses associated with recreational water usages, state governments are required by the Beaches Environmental Assessment and Coastal Health Act (BEACH) to conduct beach monitoring programs and assess potential risks using fecal indicator bacteria (FIBs) (2). Another important issue concerns the sources of beach contamination. Potential primary sources of beach contamination usually include rainfall events, sewage outflows (3), birds and other animal feces (4), human activities and leaking septic systems. Heavy rainfall (5) or onshore wind events can significantly increase the contamination level. The fecal indicator bacteria may also come from secondary sources in the environment; for example, beach foreshore sands have been widely reported to harbor high levels of indicator organisms.