With the rapid increase of technological capabilities, particularly in processing power and speed, the usage of machine learning is becoming increasingly widespread, especially in fields where real-time assessment of complex data is extremely valuable. This surge in popularity of machine learning gives rise to an abundance of potential research and projects on further broadening applications of artificial intelligence. From these opportunities comes the purpose of this thesis. Our work seeks to meaningfully increase our understanding of current capabilities of machine learning and the problems they can solve. One extremely popular application of machine learning is in data prediction, as machines are capable of finding trends that humans often miss. Our effort to this end was to examine the CVE dataset and attempt to predict future entries with Random Forests. The second area of interest lies within the great promise being demonstrated by neural networks in the field of autonomous driving. We sought to understand the research being put out by the most prominent bodies within this field and to implement a model on one of the largest standing datasets, Berkeley DeepDrive 100k. This thesis describes our efforts to build, train, and optimize a Random Forest model on the CVE dataset and a convolutional neural network on the Berkeley DeepDrive 100k dataset. We document these efforts with the goal of growing our knowledge on (and usage of) machine learning in these topics.

In thesis we will build up our operator theory for finite and infinite dimensional systems. We then prove that Heisenberg and Schrodinger representations are equivalent for systems with finite degrees of freedom. We will then make a case to switch to a C*-algebra formulation of quantum mechanics as we will prove that the Schrodinger and Heisenberg pictures become inadequate to full describe systems with infinitely many degrees of freedom because of inequivalent representations. This becomes important as we shift from single particle systems to quantum field theory, statistical mechanics, and many other areas of study. The goal of this thesis is to introduce these mathematical topics rigorously and prove that they are necessary for further study in particle physics.

Bdellovibrio bacteriovorus (BB) is a gram negative predatory bacteria that uses other gram negative bacteria to proliferate non-binarily. Due to the predatory nature of BB researchers have proposed to use it as a potential biocontrol agent against other gram negative bacteria. The in vivo effect of predatory bacteria on a living host lacks thorough investigation. This paper explores BB inside and outside of the C. elegans. BB acts internally by pre- infecting C. elegans with E. coli and then treating the worms with BB. After BB treatment worm survivavbility increased and morbidity decreased. Ex- ternally, BB modulated the environment around the nematode which reduced infection rates and increased nematode lifespan and survivability. Together, the internal and external results suggest BB has the capability to act as a living antibiotic acting topically and internally to reduce infection rates.

Electron Multiplying Charge Coupled Device (EMCCD) cameras are widely used for fluorescence microscopy experiments. However, the quantitative determination of biological parameters uniquely depends on characteristics of the unavoidably inhomogenous illumination profile as it gives rise to an image. It is therefore of interest to learn this inhomogenous illumination profiles that can dramatically vary across images alongside the camera parameters though a detailed camera model. In this manuscript we create a detailed model to learn inhomogeneous illumination profiles as well as learn all associated camera parameters. We achieve this within a Bayesian paradigm allowing us to determine full distributions over the unknowns.