Digital Commons Network^™

Analysing Flow Free With Pairs Of Dots In Triangular Graphs, Silin Chen

Senior Projects Spring 2023

In the puzzle game Flow Free, the player is given a n x n grid with a number of colored point pairings. In order to solve the puzzle, the player must draw a path connecting each pair of points so that the following conditions are met: each pair of dots is connected by a path, each square of the grid is crossed by a path, and no paths intersect. Based on these puzzles, this project examines pairs of points in triangular grid graphs obtained by hexagons for which Hamiltonian paths exist in order to identify which point configurations have solutions. …

True Random Number Generators, Jade Geng

Senior Projects Spring 2023

Quantum Random Number Generators(QRNGs), or True Random Number Generators, generate random numbers based on naturally unpredictable(or hard-to-predict) sources. Their unpredictability results in a broad application in cryptography and technology. Their sources range from nuclear decay gamma rays to cosmic rays, then to quantum optics. This thesis aims to explore various randomness sources and compare their efficiency by running a series of randomness tests. The specific setup for each random number generator will also be presented.

Certainty Is Wild And Weaving: Analyzing The Clouds Of Venus, Grace Sanger-Johnson

Senior Projects Spring 2023

Supposed detection of phosphine as a biosigature in the clouds of Venus has resulted in a flurry of interest in studying the potential habitability of Venus and other Venus-like exoplanets. However, there are still many unanswered questions about the planet's atmosphere. In this senior project, use spectroscopy to better understand the molecular composition and atmospheric dynamics of Venus. To do this, I analyzed partly-processed spectra from a previously unstudied infrared wavelength obtained at NASA’s Infrared Telescope Facility in July 2021. I developed multiple systems of analysis to extract information from the partly processed data and understand the consequences of this …

Geometry And Semiclassics Of Tetrahedral Grain Of Space, Santanu B. Antu

Senior Projects Spring 2023

The quantum theory of gravity has eluded physicists for many decades. The apparent contradiction between the physics describing the microscopic and the macroscopic regimes has given rise to some beautiful theories and mathematics. In this paper, we discuss some aspects of one of those theories, namely loop quantum gravity (LQG). Specifically, we discuss the discreteness of spacetime, a feature that distinguishes LQG from some of the other contending theories. After a general discussion in the introduction, we discuss the dynamics and quantization of the simplices (tetrahedra) that make up the space. The discrete geometry of these tetrahedral grains of space …

Mapping Maple Memory, Grace Derksen

Senior Projects Spring 2023

Senior Project submitted to The Division of Multidisciplinary Studies of Bard College.

Classification Of Doubly-Even Linear Binary Codes: An Analysis Of The Sagemath Implementation, Tom Gadron

Senior Projects Spring 2023

Classification of doubly-even linear binary codes involves finding and enumerating permutation equivalence classes of subspaces of the vector space F2_n . This project provides an analysis and explanation of the SageMath functions written by Robert Miller that implement the algorithm used for generating these codes.

From Sine Waves To Soundscapes: Exploring The Art And Science Of Analog Synthesizer Design, Saiqi Zhang

Senior Projects Spring 2023

Senior Project submitted to The Division of Science, Mathematics and Computing of Bard College.

Partial Emulation Of The Nintendo Game Boy, Ian Thomas Brassard

Senior Projects Spring 2023

“Emulation” is when one uses software to simulate the function of hardware. This project is a partial emulation of the Nintendo Game Boy. Specifically, it is an emulation of the Game Boy’s CPU, which is called the Sharp SM83 CPU. In the background, the reader is briefly introduced to both the function and history of emulators and their relationship to video games. The report moves on to detail the process of making this emulator, and discusses the similarities and differences between it and the original hardware. Technical details about the exact functions of the emulator are included. The process and …

Using Berries To Turn Sunlight Into Electricity: Taking Advice From Mother Nature Because She Has Already Mastered The Art Of Using Solar Energy, Quincy Ross

Senior Projects Spring 2023

As we try to stop anthropogenic climate change, we need to find energy sources that don’t involve burning fossil fuels. The Earth is constantly being hit with energy in the form of sunlight, we just need to figure out how to use it, thankfully plants have already gotten very good at photosynthesis. Solar energy is being improved at an exciting rate but has some material downsides when it comes to raw material mining. Dye sensitized solar cells, though having a lower efficiency than traditional photovoltaics open up opportunities for improving solar energy in many other aspects, such as reducing material …

Theoretical Foundations Of Quantum Computing And The Implementation Of The Quantum Fourier Transform, Natalia Dziubelski

Senior Projects Spring 2023

Quantum computing is a growing field with the potential to revolutionize computation. This thesis explores the foundations of quantum computing with specific focus on the efficacy of the Quantum Fourier Transform (QFT). The fundamentals of quantum computing were described through an explanation of quantum mechanics and the mathematics needed to understand the quantum computing model and its operations. Using IBM’s simulators and quantum processors, the QFT was implemented on a classical data set, and the results were compared to the predicted output values. It was found that the QFT simulator was able to produce results consistent with Discrete Fourier Transform, …

Logistics Planning: Putting Math To Work In A Business Setting, Michael C. Hannan

Senior Projects Spring 2023

The optimization of business procedures benefits all aspects of the product. Maximizing efficiency can lead to more profits for the business, cheaper products for the consumer, and less fuel consumption for the environment. Tracing the history of optimization, we can see that people have always strived for the most efficient way to allocate scarce resources. However, the field of optimization did not blossom until innovations in mathematics allowed us to solve a majority of real world problems. The discovery of linear and nonlinear programming in the 1940s allowed us to optimize problems that were unsolvable before. This paper introduces how …

Mathematical Structure Of Musical Tuning Systems, Shay Joel Francis Spitzer

Senior Projects Spring 2023

Over the course of history, western music has created a unique mathematical problem for itself. From acoustics, we know that two notes sound good together when they are related by simple ratios consisting of low primes. The problem arises when we try to build a finite set of pitches, like the 12 notes on a piano, that are all related by such ratios. We approach the problem by laying out definitions and axioms that seek to identify and generalize desirable properties. We can then apply these ideas to a broadened algebraic framework. Rings in which low prime integers can be …

Examining Stellate Unions, Julia Erin Crager

Senior Projects Spring 2023

Stellate neighborhoods are created by gluing half disks together along their straight edges. A 1-stellate neighborhood is a half disk, a 2-stellate neighborhood is a disk, a 3-stellate neighborhood is 3 half disks glued together to make a star-like shape, and so on. For a topological space $X$, and for each $n \in \nn$, the $n$-stellate subspace of $X$ is the set of all points in $X$ that have a neighborhood homeomorphic to an $n$-stellate neighborhood. I will be examining topological spaces called stellate unions, where each point in the space is contained in an $n$-stellate subspace for some $n …

Discussion Of Game Design And Construction Of A Videogame Utilizing Pcg, Ca, And Abm, Angel Obergh

Senior Projects Spring 2023

Over time, video games have evolved and new methods for game design have allowed infinite possibilities and creativity. Some of these methods are Procedurally Content Generation and Cellular Automata. The use of CA-PCG has allowed immersive worlds for users to explore, creating an infinite amount of content to enjoy while providing challenging and unexpected gameplay. This senior project seeks to utilize these concepts along with Agent Based Modeling to create a fun dynamic game. The results of this project will be the discussion in how game design affects the use of these algorithms.

Quandle Unification Reduces To Quandle Matching, Maximus Redman

Senior Projects Spring 2023

The purpose of this project is to show that quandle unification reduces to quandle matching. We show that any unification problem $U$ can be embedded into a matching problem $M$. If a unifier exists for $M$, then the narrowing sequence $N$ of that unifier can be refactored to $N'$ such that all of its idempotence narrowing steps involving substitutions are done last. At the moment when the narrowing sequence $N'$ needs only to do idempotence steps to unify $M$, we show that this implies a form for the embedded matching problem $U$ such that $U$ is guaranteed to have a …

Parking Garage Functions, Felicia Elizabeth Flores

Senior Projects Spring 2023

Senior Project submitted to The Division of Science, Mathematics and Computing of Bard College.

This project is about a generalization of parking functions called parking garage functions. Parking functions have been well studied, but the concept of parking garage functions is new and introduced in the project. Parking garage functions are sequences that represent the parking garage level preferences of cars which lead to all cars parking on a level after a systematic placement. We found a recursive formula for the number of sequences that are a parking garage function. We also found a closed formula for a subset of …

Algorithmic Bias Automation: The Effects Of Proxy On Machine-Learned Systems, Emely J. Galeano

Senior Projects Spring 2023

Senior Project submitted to The Division of Science, Mathematics and Computing of Bard College.

Comparing Voting Strategies In Blood On The Clocktower, Marty Graham

Senior Projects Spring 2023

This project models a social deduction game called “Blood on the Clocktower.” Simulated players act according to two different algorithms, and the results are recorded across four different variables. The results show that the two algorithms, while constrained to affecting one specific mechanic within the game, produce statistically different results. This model has the potential to be used in simulating group dynamics and modeling the efficacy of certain game strategies.

Compiling Quantum Programs, Li-Heng Henry Chang

Senior Projects Spring 2023

This thesis introduces the quantum compilation problem and develops a prototypical compiler. The problem of quantum compiling is, in essence, converting high-level human expressions of quantum programs into low-level hardware executable code. Compilers that target different hardware platforms enable portable code that can be used to benchmark hardware performance, reduce programming work and speed up development. Because quantum systems are subjected to phenomena such as noise, no-cloning and decoherence, the challenge of quantum compiling is tied to the optimization of program runtimes and the lengths of compiled sequences. For near-term intermediate scale quantum (NISQ) computers with limited hardware resources and …

Acceptable Title Pending: Probing The Limits Of Precision Measurement And Academic Assessment, Bobby King

Senior Projects Spring 2023

This is a project in two parts. The first is an attempt to impart onto the reader the necessary mental models required to understand a scientific experiment related to the improvement of gravitational wave detectors. Part one is illustrated in collaboration with Simone River Wilding, Sohpie Foley, Roma Taitwood, and Cam Goldberg.

Part two is a technical description of efforts made to reduce speckle in measurements of scattered light. Gravitational wave detection requires extremely high precision measurement, and one source of noise in the detectors is scattering off of defects and surface roughness in optical coatings. Research into the development …

Spotting K-Tricaps In Spot It!, Jenarah Skyara Lara

Senior Projects Spring 2023

The card game “SPOT IT!” consists of 55 cards, with 8 symbols appearing on each card. Every pair of cards has exactly one symbol in common, and the goal of the game is to be the first person to find this symbol. An alternate way to play the game is to find sets of 3 cards that have the same symbol in common. We will use combinatorics, probability, and finite projective geometry to analyze the structure of the game. The game “SPOT IT!” can be viewed as the projective plane of order 7. However, we can construct a similar game …

A Symbolic Music Transformer For Real-Time Expressive Performance And Improvisation, Arnav Shirodkar

Senior Projects Fall 2023

With the widespread proliferation of AI technology, deep architectures — many of which are based on neural networks — have been incredibly successful in a variety of different research areas and applications. Within the relatively new domain of Music Information Retrieval (MIR), deep neural networks have also been successful for a variety of tasks, including tempo estimation, beat detection, genre classification, and more. Drawing inspiration from projects like George E. Lewis's Voyager and Al Biles's GenJam, two pioneering endeavors in human-computer interaction, this project attempts to tackle the problem of expressive music generation and seeks to create a Symbolic Music …

From Fast Fashion To Conscious Couture : Revealing The Need For Policy In Shaping A Sustainable Fashion Industry, Mikelison D. Womack

Senior Projects Spring 2023

Senior Project submitted to The Division of Social Studies of Bard College.

Modeling Vascular Diffusion Of Oxygen In Breast Cancer, Tina Giorgadze

Senior Projects Spring 2023

Oxygen is a vital nutrient necessary for tumor cells to survive and proliferate. Oxygen is diffused from our blood vessels into the tissue, where it is consumed by our cells. This process can be modeled by partial differential equations with sinks and sources. This project focuses on adding an oxygen diffusion module to an existing 3D agent-based model of breast cancer developed in Dr. Norton’s lab. The mathematical diffusion module added to an existing agent-based model (ABM) includes deriving the 1-dimensional and multi-dimensional diffusion equations, implementing 2D and 3D oxygen diffusion models into the ABM, and numerically evaluating those equations …

Entering The Dance Input/Output Machine, Antonio James Martinez

Senior Projects Spring 2023

My goal for this project is to provide an exploration into the intersection of Computer Science and Dance. Although there are many avenues of exploration at this intersection, I decide to focus on the topic of movement, specifically the idea of movement data. With this idea, we break it apart into two subtopics: movement input and output. Throughout this project, we mainly focus on the side of input, uncovering the nuance of movement language and the information that comes with it to understand the process of motion capture. We also demonstrate the use of movement input and how others may …

Reed Log: Application For Oboists, Michał Cieślik

Senior Projects Spring 2023

Senior Project submitted to The Division of Science, Mathematics and Computing of Bard College.

Machine Learning For Video-Based Event Detection: A Cnn-Lstm Model, Nam Alex Nguyen

Senior Projects Fall 2023

In recent years, the application of machine learning methodology into event detection has become increasingly prevalent, with examples ranging from surveillance to entertainment and healthcare. This project aims to explore the classification of events in video content with practical implication of content management and archival. To develop a method for event detection, we will utilize the VidLife dataset — a dataset that captures a wide array of life events from the popular American television sitcom series 'The Big Bang Theory'. This project focuses on the development of a hybrid model that combines Convolutional Neural Networks (CNNs) with Long Short-Term Memory …

Wisdom Of Nature: Finding Tao In Water, Ziyu Xu

Senior Projects Fall 2022

Senior Project submitted to The Division of Arts of Bard College.

The Algebra Of Type Unification, Verity James Scheel

Senior Projects Spring 2022

Type unification takes type inference a step further by allowing non-local flow of information. By exposing the algebraic structure of type unification, we obtain even more flexibility as well as clarity in the implementation. In particular, the main contribution is an explicit description of the arithmetic of universe levels and consistency of constraints of universe levels, with hints at how row types and general unification/subsumption can fit into the same framework of constraints. The compositional nature of the algebras involved ensure correctness and reduce arbitrariness: properties such as associativity mean that implementation details of type inference do not leak in …

Fourth-Dimensional Education In Virtual Reality, Jesse P. Hamlin-Navias

Senior Projects Spring 2022

This project was driven by an interest in mathematics, visualization, and the budding field of virtual reality. The project aimed to create virtual reality software to allow users to interact and play with three-dimensional representations of four-dimensional objects. The chosen representation was a perspective projection. Much like three-dimensional shapes cast two-dimensional shadows, four-dimensional shapes cast three-dimensional shadows. Users of the software developed in this project could interact and experiment with these three-dimensional shadows using hand controlled inputs. The hypothesis put forward is that virtual reality is currently the best medium to teach three-dimensional and four-dimensional geometry.