A polyomino is a polygon that can be evenly subdivided into m equal sized squares. A polyomino visibility graph is a graph where each vertex is represented with a polyomino and each edge between two vertices is represented by two polyominos that see each other. In our research we restrict visibilities between polyominos by requiring one polyomino to see a set number of m squares in another polyomino to count as being seen. We find the largest fraction of squares each polyomino can see for some families of graphs
Faculty Sponsor: Josh Laison
Discipline: Mathematics
A graph G is a Fixed-m Polyomino Road Visibility Graph (FmPRVG) if G has a representation R with polyominoes, all the same size m, such that two polyominoes are adjacent in R if size of the smallest empty polyomino between them is less than or equal to m. We explore families of graphs such as complete graphs, cycle graphs, and star graphs, to determine whether they are FmPRVG using techniques such as their visibility regions and blockout regions.
Faculty Sponsor: Josh Laison
Discipline: Mathematics
Mathematical billiards is a dynamical system where a point travels inside a table and reflects off its boundary much like a physical pool table. Our research investigates defining more interesting billiard tables, such as regular k-gons, and expansions past the plane. In particular, we expand the billiard literature onto surfaces of revolution such as the sphere and pseudosphere. On such surfaces, we find launch angles for periodic orbits, orbits that loop back upon themselves, and orbit variants that do not work in the plane but are made possible in negative curvature. Orbits are simulated through a Mathematica codebase.
Faculty Sponsor: Josh Laison
Discipline: Mathematics
Homeownership is a powerful way for families to build wealth and stability. In Salem, there is an acute need for homeownership opportunities, especially for moderate-income families. Community Land Trusts (CLTs) reduce housing costs by separating the ownership of land from the ownership of a home and guaranteeing continued affordability through a resale limit. Our research addresses key areas of CLT development: Why this model? How could one get started? Operate? Work with anchor institutions? Help us transition toward a new economic system? A CLT in Salem can expand access to homeownership, increase community wealth, and help redefine economic relationships.
Faculty Sponsor: Nathan Sivers Boyce
Discipline: Economics
This project used machine learning models to calculate the distances to spiral galaxies. Models produced were based on the baryonic Tulley-Fisher Relation, a relationship between rotation speed and mass that can be used to estimate distances. The Cosmicflows-4 (CF4) dataset was used in this project, as well as simulated data based on the CF4. The simulated data was used to test models and assess their accuracy. This project’s method is innovative in that it does not require known distance target values for model training, making it far more viable for predicting distance values using real data.
Faculty Sponsor: Rick Watkins
Discipline: Physics
Even the biggest galactic structures in the universe started out as small differences in density in a mostly homogenous universe. Baryonic Acoustic Oscillations are an important contributor to the distribution of matter in the early universe. They come from the coupling of photons to baryonic matter leading to spherical shells of mass around high density spots in the early universe. These shells play important roles in the placement of galactic structure we see today. While already studied by other tools, my research studies this phenomenon with the new tool of persistent homology which detects holes in a data set.
Faculty Sponsor: Rick Watkins
Discipline: Physics
Oil-water separation technologies have proven to be an effective and eco-friendly way to combat oil-water separation problems. The study focuses on the fabrication of copper mesh using laser ablation with different scanning speeds and accessing their effectiveness through a filtration experiment using an olive oil-water mixture. This method involves finding which scanning speed looks to be the most effective for efficient oil-water separation. Although the findings of this experiment contribute to the development of technology for oil-water separation, further research is warranted to explore numerous avenues for future investigation, such as long-term durability.
Faculty Sponsor: Rick Watkins
Discipline: Physics
Research-based assessments are used by professors to gauge the knowledge of their students in different concepts. By understanding their students, they can adapt their teachings to fit them. Many assessments are being created and altered by people in the physics education community. A change in these assessments is avoiding traditional scoring. Couplet scoring gives information on what students know even if they choose the incorrect answers. In this thesis, we apply couplet scoring to a popular physics assessment and compare our scoring scheme to others. We analyze data using our scoring and provide these results to the physics education community.
Faculty Sponsor: Michael Vignal
Discipline: Physics
This research focuses on machine learning and the interdisciplinary field of chaos theory, which studies systems that can often appear random but are driven by deterministic forces. They are particularly difficult to predict because of how sensitive they are to tiny variations. To study these we use a type of chaotic pendulum called a mechanical chaotic oscillator (MCO), which creates chaotic conditions and records data all in one place. By combining the MCO data and simulated data, we train machine learning algorithms intending to surpass the current limitations of traditional prediction approaches.
Faculty Sponsor: Daniel Borrero
Discipline: Physics
A chaotic system is a system of equations that has unpredictable outputs with no apparent pattern. This is due to an important aspect of this system which is its sensitivity to initial conditions. In this thesis, I will focus on a specific chaotic system known as the Lorenz system. After many attempts, I successfully recreated the Lorenz system in analog electronic form. I then began to focus on the synchronization property of this system which would allow me to explore this system's private communication application.
Faculty Sponsor: Daniel Borrero
Discipline: Physics
When using lasers to study the minuscule forces generated by the molecular engines of cells, even the smallest vibrations and deviations in alignment can drastically affect your measurements. Motivated by the discovery of low-frequency mechanical noise and misaligned lenses in the Altman Lab's optical tweezers apparatus, I re-designed several key components that were machined and installed. In this presentation, I will describe the 3-D design process and present preliminary characterization of the modified system, including an application of Allan variance to quantify low-frequency noise and new methods to determine within what region of the detector we can collect meaningful data.
Faculty Sponsor: David Altman
Discipline: Physics
This project aims to understand the role of myosin VI, a molecular motor, on the viscoelastic properties of cultured retinal pigment epithelium (RPE) cells. It examines the role of myosin VI in photoreceptor outer segment phagocytosis by RPE cells. We know it’s involved in this process, but we don’t know how. In other cell systems, myosin VI is known to behave as either a transporter and or a cross-linker. This work uses an optical trap to perform microrheology to test whether its role in RPE cells include that of a cross-linker, regulating the material properties of the cell interior.
Faculty Sponsor: David Altman
Discipline: Physics
Our research focuses on myosin II, a cytoskeletal motor protein capable of generating motion inside cells. Because these motors function in an incredibly crowded and dynamic cellular environment, they experience a variety of forces in various directions. This project aims to understand how such forces can regulate the motor’s activity. Using an optical trap, a tightly focused laser that can apply forces to microscopic objects, we measured how myosin’s stepping varies in response to forces applied in different directions. Preliminary single-molecule data suggest that myosin’s motility is dependent on the magnitude and direction of the forces it experiences.
Faculty Sponsor: David Altman
Discipline: Physics