Computer vision is a branch of artificial intelligence that involves applications of mathematical methods and computers for machine learning from digital images and videos. Here, we apply computer vision-based methods for optical character recognition (OCR) and image compression. OCR has important applications such as process automation like check clearing, digitizing text and image records for online databases, automated analysis of surveillance camera videos for security, automated reading of text from car license plates in a parking lot, etc. But how can we feed visual information to a computer in a form that it can understand and operate on? To this end, we digitized images into vectorized arrays and analyzed data using vector and scalar projections. Further, we applied algorithms with foundations in linear algebra and wrote programs using Python scientific libraries for optical character recognition and image compression. Using IPython, we characterized color and grayscale images as arrays and implemented singular value decompositions (SVD) and principal component analysis (PCA) for grayscale and color image compression studies and OCR. These studies illustrate how mathematical transformations and data reduction methods can be used for optical character recognition, image compression, identification and encryption. This project elucidates the key role of mathematical modeling for computer vision applications.

The thermal optimization of computer systems is a study dating back to their creation. Because powerful computers typically generate additional heat, the more heat one can remove from a computer, the more powerful they can make it. Over the years, it has become a popular solution for many companies to build computers using standardized, modular hardware. Our research questions the cooling efficiency of this standardized hardware. Initially, we are creating a 3D simulation of a desktop computer that will allow us to quickly test various internal component layouts for thermal efficiency. Using a custom-programmed microcontroller for data collection, our real-world testing includes the building and monitoring of both a computer built in this standardized fashion and one reconfigured to other custom layouts, which, from our simulations, we anticipate will improve the cooling capabilities of the computer. By using this data in conjunction with observations from our digital 3D simulations, we hope to test potential improvements to the layout of computer components to enhance the performance of both high-end computers and everyday desktops.

The design of quantum computers using Nitrogen vacancies in diamond has renewed interest in providing a microscopic understanding of the properties of the various allotropes of carbon. Here we visualized the crystal structure and electron densities of diamond, graphite, and fullerene to understand the novel structures and bonding in these materials. Using vector calculus-based methods, we computed the bond lengths and bond angles of diamond, graphite, and fullerene. While diamond exhibited sp3 bonding, both graphite and fullerene revealed sp2 bonding. These key changes in structure and bonding gave rise to important differences in their brightness, hardness, electrical conductivity, etc. We computed the adjacency matrix of fullerene and used that to understand the network connectivity. These studies provided an atomic level understanding of the structure, bonding, adjacency matrix, and network connectivity in these materials which form essential inputs and aid in the design of quantum computers.

This research analyzes how vagal nerve stimulators have been used for treatment of Crohn’s Disease through literary review of existing research in order to assess what is working and begin to remedy what can be improved in order to increase the likelihood of remission for patients. The analysis of this research includes assessment of the design of current vagal nerve stimulators, materials used, algorithmic architecture behind the device, as well as methods of testing and measuring results. The methods used to determine success of remission include patient surveys, measurements of mucosal metabolites, assessment of cytokine levels, and others. Could vagal nerve stimulators be improved to work better with the brain, and therefore increase the remission rate to nearly absolute? From the analysis, it seems so -- however, there are enhancements that need to be made in materials, technology, and communication. The continuing advancement in vagal nerve stimulation therapy could potentially lead to a consistent, low-risk, accessible cure for Crohn’s Disease.