This research endeavor explores the 1964 reasoning of Irish physicist John Bell and how it pertains to the provoking Einstein-Podolsky-Rosen Paradox. It is necessary to establish the machinations of formalisms ranging from conservation laws to quantum mechanical principles. The notion that locality is unable to be reconciled with the quantum paradigm is upheld through analysis and the subsequent Aspect experiments in the years 1980-1982. No matter the complexity, any local hidden variable theory is incompatible with the formulation of standard quantum mechanics. A number of strikingly ambiguous and abstract concepts are addressed in this pursuit to deduce quantum's validity, including separability and reality. `Elements of reality' characteristic of unique spaces are defined using basis terminology and logic from EPR. The discussion draws directly from Bell's succinct 1964 Physics 1 paper as well as numerous other useful sources. The fundamental principle and insight gleaned is that quantum physics is indeed nonlocal; the door into its metaphysical and philosophical implications has long since been opened. Yet the nexus of information pertaining to Bell's inequality and EPR logic does nothing but assert the impeccable success of quantum physics' ability to describe nature.

The use of enzyme-catalyst interfaces is underexplored in the field of biocatalysis, particularly in studies on enabling novel reactivity of enzymes. For this thesis, the HaloTag® protein tagging platform was proposed as a bioconjugation method for a pinacol coupling reaction using lipases, as a model for novel reactivities proceeding via ketyl radical intermediates and hydrogen-bonding-facilitated redox attenuation. After an initial lipase screening of 9 lipases, one lipase (Candida rugosa) was found to perform the pinacol coupling of p-anisaldehyde under standard conditions (fluorescein and 530nm light, 3% yield). Based on a retrosynthetic analysis for the photocatalyst-incorporated HaloTag® linker, the intermediates haloamine 1 and aldehyde 6 were synthesized. Further experiments are underway or planned to complete linker synthesis and conduct pinacol coupling experiments with a bioconjugated system. This project underscores the promising biocatalytic promiscuity of lipases for performing reactions proceeding through ketyl radical intermediates, as well as the underdeveloped potential of incorporating bioengineering principles like bioconjugation into biocatalysis to overcome kinetic barriers to electron transfer and optimize biocatalytic reactions.

Stardust grains can provide useful information about the Solar System environment before the Sun was born. Stardust grains show distinct isotopic compositions that indicate their origins, like the atmospheres of red giant stars, asymptotic giant branch stars, and supernovae (e.g., Bose et al. 2010). It has been argued that some stardust grains likely condensed in classical nova outbursts (e.g., Amari et al. 2001). These nova candidate grains contain 13C, 15N and 17O-rich nuclides which are produced by proton burning. However, these nuclides alone cannot constrain the stellar source of nova candidate grains. Nova ejecta is rich in 7Be that decays to 7Li (which has a half-life of ~53 days). I want to measure 6,7Li isotopes in nova candidate grains using the NanoSIMS 50L (nanoscale secondary ion mass spectrometry) to establish their nova origins without ambiguity. Several stardust grains that are nova candidate grains were identified in meteorite Acfer 094 on the basis of their oxygen isotopes. The identified silicate and oxide stardust grains are <500 nm in size and exist in the meteorite surrounded by meteoritic silicates. Therefore, 6,7Li isotopic measurements on these grains are hindered because of the large 300-500 nm oxygen ion beam in the NanoSIMS. I devised a methodology to isolate stardust grains by performing Focused Ion Beam milling with the FIB – Nova 200 NanoLab (FEI) instrument. We proved that the current FIB instrument cannot be used to prepare stardust grains smaller than 1 𝜇m due to lacking capabilities of the FIB. For future analyses, we could either use the same milling technique with the new and improved FIB – Helios 5 UX or use the recently constructed duoplasmatron on the NanoSIMS that can achieve a size of ~75 nm oxygen ion beam.

Debris disks are a collection of dust grains and planetesimals around a star and are thought to contain the remnants of planet formation. Directly imaging debris disks and studying their morphologies is valuable for studying the planet formation process. In some stellar systems that have a directly imaged debris disk, there are also directly imaged planets. Debris disk structures like gaps and asymmetries can show the gravitational e↵ects of planets that are below the brightness threshold for being detected via direct imaging. We investigate a sample of debris disks in Scorpius-Centaurus (Sco-Cen) that were imaged with the Gemini Planet Imager (GPI), which is an adaptive optics system with a coronagraph to block starlight. We look at two GPI data sets, the GPIES campaign Sco-Cen targets, and a follow-up observing program for Sco-Cen targets. We resolve 5 debris disks in the follow-up program and 13 from the GPIES campaign. By calculating contrast curves, we determine the planet detection limit in each of the GPI images. We find that we could have detected 5 Jupiter mass planets at angular separations greater than about 0.6 arcseconds in our GPIES campaign images. In three of our images we could have detected 2 Jupiter mass planets in wide orbits, but 2 Jupiter masses below the detection limit in our other images. We identify one point source around HD 108904 as a sub-stellar companion candidate. To further check for evidence of planets that are below the detection limit, we measure the surface brightness profile of the disks to check for asymmetries in brightness. We find that one of the edge-on disks has an asymmetric surface brightness profile, HD 106906, and three other edge-on disks have symmetric surface brightness profiles. We also find that two disks, HD 106906 and HD 111520, are asymmetric in radial extent, which is possibly evidence for gravitational interactions with planets.

This thesis project focuses on algorithms that generate good sampling points for function approximation. In one dimension, polynomial interpolation using equispaced points is unstable, with high Oscillations near the endpoints of the interpolated interval. On the other hand, Chebyshev nodes provide both stable and highly accurate points for polynomial interpolation. In higher dimensions, optimal sampling points are unknown. This project addresses this problem by finding algorithms that are robust in various domains for polynomial interpolation and least-squares. To measure the quality of the nodes produced by said algorithms, the Lebesgue constant will be used. In the algorithms, a number of numerical techniques will be used, such as the Gram-Schmidt process and the pivoted-QR process. In addition, concepts such as node density and greedy algorithms will be explored.

The COVID-19 pandemic has resulted in preventative measures and has led to extensive changes in lifestyle for the vast majority of the American population. As the pandemic progresses, a growing amount of evidence shows that minority groups, such as the Deaf community, are often disproportionately and uniquely affected. Deaf people are directly affected in their ability to personally socialize and continue with daily routines. More specifically, this can constitute their ability to meet new people, connect with friends/family, and to perform in their work or learning environment. It also may result in further mental health changes and an increased reliance on technology. The impact of COVID-19 on the Deaf community in clinical settings must also be considered. This includes changes in policies for in-person interpreters and a rise in telehealth. Often, these effects can be representative of the pre-existing low health literacy, frequency of miscommunication, poor treatment, and the inconvenience felt by Deaf people when trying to access healthcare. Ultimately, these effects on the Deaf community must be taken into account when attempting to create a full picture of the societal shift caused by COVID-19.

Lyme disease is a common tick-borne illness caused by the Gram-negative bacterium Borrelia burgdorferi. An outer membrane protein of Borrelia burgdorferi, P66, has been suggested as a possible target for Lyme disease treatments. However, a lack of structural information available for P66 has hindered attempts to design medications to target the protein. Therefore, this study attempted to find methods for expressing and purifying P66 in quantities that can be used for structural studies. It was found that by using the PelB signal sequence, His-tagged P66 could be directed to the outer membrane of Escherichia coli, as confirmed by an anti-His Western blot. Further attempts to optimize P66 expression in the outer membrane were made, pending verification via Western blotting. The ability to direct P66 to the outer membrane using the PelB signal sequence is a promising first step in determining the overall structure of P66, but further work is needed before P66 is ready for large-scale purification for structural studies.

The colossal global counterfeit market and advances in cryptography including quantum computing supremacy have led the drive for a class of anti-counterfeit tags that are physically unclonable. Dendrites, previously considered an undesirable side effect of battery operation, have promise as an extremely versatile version of such tags, with their fundamental nature ensuring that no two dendrites are alike and that they can be read at multiple magnification scales. In this work, we first pursue a simulation for electrochemical dendrites that elucidates fundamental information about their growth mechanism. We then translate these results into physical dendrites and demonstrate methods of producing a hash from these dendrites that is damage-tolerant for real-world verification. Finally, we explore theoretical curiosities that arise from the fractal nature of dendrites. We find that uniquely ramified dendrites, which rely on lower ion mobility and conductive deposition, are particularly amenable to wavelet hashing, and demonstrate that these dendrites have strong commercial potential for securing supply chains at the highest level while maintaining a low price point.

Treatment log files for spot scanning proton therapy provide a record of delivery accuracy, but they also contain diagnostic information for machine performance. A collection of patient log files can identify machine performance trends over time. This facilitates the identification of machine issues before they cause downtime or degrade treatment quality. At Mayo Clinic Arizona, all patient treatment logs are stored in a database. These log files contain information including the gantry, beam position, monitor units (MUs), and gantry angle. This data was analyzed to identify trends, which were then correlated with quality assurance measurements and maintenance records.

The reionization of the Universe is thought to have completed by redshift z~5.5. To probe this era, galaxy observations in the Subaru Deep Field (SDF) have identified more than 100 galaxies at z~6, many spectroscopically confirmed through follow-up observations. Using available optical/IR data, we model with CIGALE the spectral energy distributions (SEDs) of 43 SDF galaxies, including newly acquired data from the UKIRT WFCAM K-band for seven previously studied objects. In particular, modeling deep IR photometry is sensitive to the galaxy's Lyman continuum (LyC) escape fraction (fesc). We find the median implied fesc value as ~0.4+/-0.1 (mean error). Significant uncertainties in data and fitting result in a large range of fesc for individual objects, but analysis suggests that fesc is likely high enough for galaxies to finish reionization by z~6. More importantly, we find trends between the CIGALE UV slope b, fesc, and dust extinction E(B-V): for a given E(B-V), b appear steeper by ~0.4 than at z=0. Lower fesc values appear to be associated with bluer b and lower E(B-V), but only weakly. This suggests that LyC could have escaped through holes with sufficiently wide opening angles surrounding the ISM from outflows of supernovae and/or weak AGN to escape, but resulting in a large range of implied fesc values depending on the orientation of each galaxy. The current HST, Spitzer and ground-based photometric and model errors for the 43 galaxies are large, so IR spectroscopic observations with the James Webb Space Telescope are needed to better constrain this possibility.