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.

Rotary encoders are present in many electronic devices, and are used to measure changes in rotation. The common photo type encoder has remained largely unchanged in its fundamental operation, and faces limitations in resolution at small sizes. This research explores an encoder design utilizing polarizers, that can achieve higher resolutions than similarly sized photo encoders. Current photo encoders achieve their rotational measurements through a rotating disk, with perforations located along the circumference. As the disk rotates, a photodiode receives pulses of light through the perforations from a light source. The resulting signal(s) consists of a multitude of digital pulses that require compiling and processing, before position can be determined. To achieve higher resolutions, more perforations are required, and more photodiodes are needed. High-resolution encoders can therefore become very expensive as the perforations increase, and the perforations, and therefore resolution, is limited at smaller sizes. However, there is a way to inexpensively achieve indefinite resolution and absolute position, at sizes that are unfeasible with current encoder technologies. Such an encoder utilizes an initially polarized light source, followed by an analyzer polarizer, and then a photodiode. As the analyzer is rotated, the photodiode receives a gradually increasing, and then decreasing, change in brightness (translating into current). Rotating the analyzer continuously, produces a sine graph of current change, with each point corresponding to a position of the analyzer. In this research, this configuration has been adapted to create a small scale, and high-resolution rotary encoder. This polarizer encoder measures only ten millimeters in diameter, and achieves greater resolution than current similarly sized rotary encoders.

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.

The structure and function of a protein is determined by the amino acid sequence that makes up the protein. Understanding how proteins are likely to mutate allows us to predict how organisms will evolve. However, the complex interactions between amino acids in a protein makes it difficult to predict beneficial mutations, and specifically their impact on protein function. I introduced models grounded in statistical physics to learn effective couplings between protein residues from evolutionary data and infer the impact of mutations using covariation of amino acids in evolutionary samples. I then compared the inferred model with machine learning inference of biophysical interactions in proteins that our team has developed to characterize the amino acid preferences within structural micro-environments of proteins. The results of this project will allow us to combine evolutionary data and machine learning inferences to predict beneficial mutations that will occur in a protein. This would have myriad benefits in medicine and evolutionary biology such as being able to predict how bacteria and viruses are likely to mutate in response to treatments.

Current physics education research has demonstrated that, when not taught directly, students have a wide range of conceptual resources regarding the use of variables upon entering introductory physics. There is a growing body of work that characterizes students’ use of variables and how students connect variables to their physical meaning (Brahmia 2019). We build on this work by seeking to better understand how students are making sense of variables in introductory physics labs. Data was collected from students’ responses to lab curriculum on the online lab platform, Pivot Interactives, from the 2020-2021 academic year. By examining students’ variable choice when graphing experimental data over the course of a quarter, we are able to identify emerging commonalities in variable use and how the variables students choose correlates with the students’ broader understanding of quantitative reasoning. Preliminary data from student graphs of position versus time show a prevalence of students using math-like variables, such as y and x, instead of variables traditionally used to represent these quantities in physics, such as x to represent position and t to represent time. Use of math-like variables in a physical context suggests that these students’ may have not yet formed a strong association between the variable itself and the meaning of the physical quantity it represents. Insights into student variable use and its relationship to the students’ overall quantitative reasoning can help instructors consider effective methods that adapt curriculum to directly address the use and meaning of variables within physics. By doing so, instructors may have an opportunity to directly impact their students’ quantitative reasoning – a skill valued across all STEM disciplines.

Trapped ions is an approach to quantum computing that proposes to store qubits in the stable electronic states of ions. These qubits transition from one state to another by absorbing or emitting photons. This process is known as quantum jumps. The absorption and emission of photons by individual ions become coherent processes at sufficiently small separations. The goal of our project was to observe these collective effects by observing the quantum jump rate in systems of multiple ions. We identified quantum jumps by observing sudden changes in the number of photons emitted by an ion. In our preliminary analysis we found a proportional relationship between the quantum jump rate and the number of ions in a chain. However, due to the presence of noise from neighboring ions, our results had significant errors. To minimize the randomness introduced by noise, we counted the number of photons in small intervals of “integration time” and evaluated the optimal transition rate by minimizing incorrect identification of jumps. We hypothesize that the transition rate of ions depends on the number of ions in our system. A deeper understanding of quantum jumps may possibly help us control them and eventually be used to correct errors in quantum computing involving trapped ions.

Semi-visible Jets may occur from strongly coupled hidden sectors produced at the Large Hadron Collider, as suggested in the Hidden Valley models. While dark hadrons interact strongly with each other, they interact only weakly with visible states through the portal, which will undergo a QCD-like shower and ultimately hadronize, producing collimated sprays of dark hadrons. These states are invisible to colliders’ detectors unless they are able to decay to the Standard Model. A portion of these states are likely to be stable, providing good dark-matter candidates. Yet, many of the hadrons should decay back to the visible sector through the portal coupling, which result in a spray of stable invisible dark matter along with unstable states that decay back to the Standard Model. The signature of such Semi-visible Jets is characterized by the missing energy aligned along the direction of one of the jets. In this research, we generated the Semi-visible Jets s-channel samples using standalone MadGraph5, Pythia8, and Delphes and conducted data analysis using uproot and pyjet package in Python. We analyzed the kinematics of Semi-visible Jets with different parameter settings such as event selection cuts and jet clustering algorithms by creating kinematic plots of physical quantities including jet momentum, invariant mass, transverse mass, and missing energy using Python. Also, we have created the ATLAS JobOption, which has already been used for sample generation in the CERN ATLAS framework. We have noticed differences in kinematic distribution with different event selection and jet clustering algorithms and we expect to find the parameter settings for them that will optimize the Semi-visible Jets signal. By applying optimized parameter settings, we can locate the possible region where Semi-visible Jets can be observed in the Large Hadron Collider, which is a significant step forward in the discovery of dark matter.

Detecting physics beyond the standard model is an important task that utilizes cutting edge new models. In the “Anomaly Detection Data Challenge 2021,” we develop a novel anomaly detection algorithm for the task of finding a priori unknown and rare New Physics data. The challenge uses simulated anomaly detection data that emulates the strict bandwidth, latency and resource constraints of the L1 trigger of the Large Hadron Collider whose dataset is composed of 10 particle jets, 4 muons, 4 electrons, and missing transverse energy. Autoencoders and variational autoencoders are powerful neural network models that are widely used to approximate input distributions and reduce latent dimensions. We reproduce simple autoencoders/variational autoencoders to detect anomalies within the dataset using Mean Squared Error (MSE) loss and Kullback- Leibler divergence (K-L Divergence) as the anomaly metrics respectively. Using these well-performing autoencoder models as a baseline, we develop and test novel, powerful, generative and autoencoder based models for the anomaly detection task.

In this project, we measure electron flow in graphene, a 2-D lattice of carbon atoms, and compare the results to simulations. As current is passed through typical electrical devices, the electron’s diffusion is dominated by collisions with impurities in the atomic lattice, giving rise to the material's resistance, the opposition to flow. This is called ohmic conduction. However, clean graphene permits a more dynamic and exciting type of conduction-- the hydrodynamic regime. Here, electrons’ collisions with each other are significant, and their collective behavior becomes water-like. When measured over a range of temperatures, we find dips in the resistance, resulting from these hydrodynamic electrons’ tendency to “pull” one another along with the bulk. Like honey, these electrons have viscosity, which unlike resistance, is a property of the fluid. This research will further elucidate properties of the electron fluid. To complete this project, we fabricate graphene devices and study them in a table-top cryostat, measuring the current profile from 4K to room temperature. We are particularly interested in how this viscous fluid behaves as it encounters a boundary within the device, an open question in the field. Using a unique homebuilt experimental instrument, called the feedback-lockin amplifier, we visualize the flow of electrons around a small scan probe tip. Comparison with python simulations helps us elucidate the fluid's boundary conditions. This research will directly benefit the electronics industry. The next generation of computer chips will utilize 2-D materials such as graphene, potentially enabling the useful properties of hydrodynamic flow to be harnessed. For example, the reduced resistance inherent to hydrodynamic conduction may increase the power efficiency of transistors.

Magnetoencephalography (MEG) is a powerful noninvasive technique for measuring the location of brain activity in real time. MEG is used today in research and clinical settings around the world, and is especially advantageous for measurement on children. An array of highly sensitive sensors outside the skull measures the magnetic field produced by current in the brain. Algorithms then localize this synaptic current via a process called the magnetic inverse problem. Critical to this challenge are assumptions intrinsic to the equations that describe magnetic fields. This project explores the assumptions and fundamental structure of major equations used in MEG today. By performing simulations and mathematical modeling we shed light on the interpretations of MEG signal as well as scrutinize what types of synaptic current MEG is capable of seeing. The ultimate goal of our exploration is to help researchers, neuroscientists, and clinicians understand the power and limitations of MEG and make accurate and meaningful claims.

What does it mean to grasp an object and feel it to be “cold?” You aren’t gaining cold; you are losing heat as it transfers out of you and into the object. Likewise, air conditioners transfer heat out of rooms and refrigerators transfer heat out of food. Most refrigerators and air conditioners are vapor compressors, meaning they transfer heat by compressing a toxic substance called refrigerant, which rapidly condenses and evaporates. This project demonstrates a simpler and cheaper method of heat transfer using thermoacoustics. Thermoacoustic refrigerators (TAR) have been researched for decades but only used in niche applications like onboard the Space Shuttle. We hope that our findings can drive commercial development. Our TAR has 4 main components: transducer, resonator, stack, and heat exchangers. The transducer is a loudspeaker that generates a standing wave inside a PVC pipe resonator. The stack is a plastic 3D-printed cylinder with internal parallel plates. A phenomenon called the “Brayton cycle” uses the sound waves to pump heat and generate a temperature gradient across the stack, making one end cold and the other hot. The cold heat exchanger brings in air that needs to be cooled and transfers heat from it into the stack, while the hot heat exchanger cools down the hot end of the stack. The actual sound waves at the stack are disrupted by the resonator tube, heat exchangers, and the stack itself. This decreases the slope of the temperature gradient. Some research has been done on the effects of different speaker input waveforms (sine, square, triangle, etc.) but not on cancelling out the disruption. Therefore, we will use signal processing to find the proper speaker input waveform that corrects this disruption. Our MATLAB simulations and theory lead us to expect that this should generate a steeper gradient and thus better cooling.

Quantum sensing platforms based on ensembles of nitrogen-vacancy (NV) centers in diamond enable high-sensitivity magnetic field detection at room temperature, making them uniquely suited for studying biological systems. Our work leverages the advantages of this diamond-NV sensing platform to directly measure the bend stiffness of individual DNA molecules using quantum-enabled magnetic imaging. In our experiment, a single DNA molecule is tethered to the surface of a diamond-NV sensor at one end and adhered to a ferromagnetic nanoparticle at the other end. A magnetic tweezer is used to apply a torque on the magnetic particle which bends the DNA strand in an effort to align the nanoparticle’s magnetic moment with the applied magnetic field. Quantum control and microscopy of the NV centers subsequently allows us to image the particle’s magnetic dipole field and the total applied field. Any deviation of the particle’s magnetic moment vector from the applied field vector can then be attributed to an opposing torque exerted by the DNA on the magnetic particle. Thus, measuring the difference between these vectors allows for the measurement of DNA bend stiffness. With this project, I detail the use of optically detected magnetic resonance and magnetic field image analysis to accurately measure the components of the aforementioned vectors. Additionally, I explore the limits of the diamond-NV platform in sensing the applied magnetic field in a highly symmetric configuration. Prior measurements have inferred the bend stiffness of DNA from statistical measurements such as cyclization. The novel direct measurement of DNA bend stiffness enabled by this project will help the scientific community understand sequence-dependent DNA flexibility, which plays a key role in biological processes such as eukaryotic nucleosomal compaction, viral genome packaging, and transcription regulation.