Since Computed Tomography (CT) scans expose the patients to high x-ray radiation dose which may potentially induce lifetime risk of cancers, researchers have been finding ways to reduce the radiation dose while maintaining the high quality of reconstructed images. One approach to lower the total X-ray radiation dose is to reduce the number of projections acquired, which generated sparse-view CT image. However, when the number of view angles is too less to satisfy the Shannon/Nyquist sampling theorem, serious streaking artifacts will appear on the reconstructed images. In this work, we present two iterative reconstruction algorithms, which implement convolutional neural networks (CNN) in each iterative step, to help eliminate these defects. The first algorithm is LEARN, which uses a CNN in place of a regularization function while solving a least squares problem. The second algorithm is based on SART and the superiorization methodology (an iterative method for constrained optimization), where the CNN is used to perturb the solution between SART iterations. We use Tensorflow and the Pyro-NN library in Python to train on data obtained from The Cancer Imaging Archive’s QIN LUNG CT dataset, and compare the performance of these two frameworks from the perspectives of PSNR value (often used to exam the quality of an image), training loss, penalty term, and learning rate. Besides testing on different sparse-view imaging datasets, we also demonstrate the performance of the proposed networks in limited angle CT image, where some view angles are missing due to geometric constraints.

Data encryption finds important applications in cybersecurity and is vital for sensitive data including online financial transactions, preventing data breach from social media platforms, data security, etc. We have used various mathematical algorithms using matrix algebra for data encryption. We have developed a phone app for secure data transmission and relay which is suitable for data encryption for email, internet and social media. We have used static and dynamic data encryption as well as data scrambling methods to provide additional layer of security. The methods we use are suitable for storage and transmission of text, images, audio and video on the internet. The algorithms we employ include Hill Cipher, Modulo arithmetic, hash functions, random data shuffling, data scrambling, LU factorization and other linear algebra methods for data encryption. We have studied advanced encryption standards (AES) used for compliance for financial processing. We propose mathematical algorithms involving end-to-end data encryption which may be suitable for video data relay or online data processing for banking, credit card and other financial transactions. The project provides real-world applications of Mathematics for Cybersecurity and Data Sciences.

 Solar power provides a renewable energy resource that reduces carbon footprints and lowers global warming. Solar panels use photovoltaics which convert light to electricity. Most commercial solar panels use silicon wafers. Electrons in these semiconducting silicon panels are freed by solar energy and are induced to travel through an electrical circuit, powering electrical devices or sending electricity to the grid. We have analyzed the reported crystal structure of silicon, which crystallizes in the same pattern as diamond and has a face centered cubic structure with lattice constant 5.4307 Å. We employed vector calculus-based methods to calculate the nearest-neighbor bond lengths (2.3516 Å) and bond angles (109.471^o) of crystalline silicon. These calculated bond-lengths and angle values are in good agreement with reported data. We visualized the electronic charge-density of silicon. Using vector-calculus based methods, we derived the equation for the plane of the solar panel and estimated the power that a solar panel can produce. Real time data from solar panel grids are currently available from energy databases. We determined the total energy produced by a solar panel array over the course of a day by finding the area under the power-vs-time real-time data reported in energy databases using integral calculus-based methods. To understand seasonal variations, we compared solar energy production on a hot summer day and during an overcast winter day. Our studies provide a microscopic atomic level understanding of solar energy and provides an integrated study of mathematics with solar physics and engineering.

Understanding cause-and-effect is key for informed decision-making. The gold standard in causal inference is performing controlled experiments, which may not always be feasible due to ethical, legal, or cost constraints. As an alternative, inferring causality from observational data has been extensively used in statistics and social sciences. However, the existing methods critically rely on a restrictive assumption that the population of study consists of homogeneous units that can be represented as a single flat table. In contrast, in many real-world settings, the study domain consists of heterogeneous units that are best represented using relational databases. We propose and demonstrate CaRL: an end-to-end system for drawing causal inference from relational data. In addition, we built a visual interface to wrap around CaRL. In the demonstration, I will use CaRL, which I have implemented, to show a live investigation of causal inference from real academic and medical relational databases.

Localization, mapping, and navigation are common tasks in robotics but, in the case of robots with limited sensors and processing power, these tasks can be difficult to reliably achieve. Particularly in the field of personal robotics, robots are often built with limited capabilities in the interest of making them more affordable. This increases the likelihood that such robots will fail at various components of its navigation tasks. To address this, we propose developing a robot that can determine when it has failed, intelligently ask humans for help in such scenarios, and learn from that help to better address these scenarios in the future. To achieve this goal, we will develop a web-based teleoperation interface for Kuri, a relatively simple personal robot. Challenges involved in this goal are the reduction of video latency between Kuri and its interface as well as how to design the teleoperation interface to make it easy for humans to use. Such an interface will make it possible for humans to directly interact with the Kuri and aid it in difficult situations. This teleoperation interface will be one of multiple strategies that Kuri will use to ask humans for help. These strategies include explicitly asking a human to tell Kuri where it is through a text or even speech interface or, similarly, answering other queries that help Kuri in understanding its environment. We will then run experiments to determine how willing humans are to provide different types of help to Kuri, how useful each type of help is to the robot, and in what scenarios the robot should utilize each type of help. This project will help us understand to what extent human aid can make navigation easier for robots and, ultimately, this will further bridge the gap between humans and robots in personal environments.

Augmented reality (AR) technologies, which overlay digital content atop the user’s perception of the real world, are on the brink of pervasive commercial deployment. AR brings new modes of interaction, eliciting unique user expectations and behaviors, but its user-facing security and privacy challenges remain underexplored. In particular, my work identifies multi-user AR – which includes such compelling use cases as in-person collaborative tools, multiplayer gaming, and telepresence – as containing many unsolved problems in handling users’ malicious or careless behavior. In this talk, I discuss my work on security and privacy for multi-user AR interactions, spanning methodologies from studying users to threat modeling to system building. I argue that AR’s physical-world integration drives novel user expectations, that navigating this physicality poses crucial challenges for supporting secure and private AR content sharing, and that these challenges pose fundamental design questions that must be addressed while the technology is still nascent. I show that the security and privacy properties of an AR interaction are tied to interaction semantics, motivating a flexible AR content sharing module that can support many application needs. I systematize security and functionality design goals for such a module, and I design and prototype ShareAR, an application-level module for the Microsoft HoloLens that meets these goals. I demonstrate that ShareAR can meet the security and functionality needs of a range of applications in relatively few lines of code and with low performance overhead. The ShareAR code is publicly available and has been qualitatively tested by two undergraduate developers. In addition to directly supporting secure multi-user AR interactions, this work provides a scaffold for defining security and privacy for multi-user AR interactions, opening directions for future work in this space. By building foundations for secure multi-user AR content sharing, my work takes steps toward allowing AR to securely reach its full potential.