Physical Sciences and Mathematics Commons^™

On The Tropicalization Of Lines Onto Tropical Quadrics, Natasha Crepeau

HMC Senior Theses

Tropical geometry uses the minimum and addition operations to consider tropical versions of the curves, surfaces, and more generally the zero set of polynomials, called varieties, that are the objects of study in classical algebraic geometry. One known result in classical geometry is that smooth quadric surfaces in three-dimensional projective space, $\mathbb{P}^3$, are doubly ruled, and those rulings form a disjoint union of conics in $\mathbb{P}^5$. We wish to see if the same result holds for smooth tropical quadrics. We use the Fundamental Theorem of Tropical Algebraic Geometry to outline an approach to studying how lines lift onto a tropical …

Going Meta On The Minimum Circuit Size Problem: How Hard Is It To Show How Hard Showing Hardness Is?, Zoë Bell

HMC Senior Theses

The Minimum Circuit Size Problem (MCSP) is a problem with a long history in computational complexity theory which has recently experienced a resurgence in attention. MCSP takes as input the description of a Boolean function f as a truth table as well as a size parameter s, and outputs whether there is a circuit that computes f of size ≤ s. It is of great interest whether MCSP is NP-complete, but there have been shown to be many technical obstacles to proving that it is. Most of these results come in the following form: If MCSP is NP-complete …

On Rank-Two And Affine Cluster Algebras, Feiyang Lin

HMC Senior Theses

Motivated by existing results about the Kronecker cluster algebra, this thesis is concerned with two families of cluster algebras, which are two different ways of generalizing the Kronecker case: rank-two cluster algebras, and cluster algebras of type A_n,1. Regarding rank-two cluster algebras, our main result is a conjectural bijection that would prove the equivalence of two combinatorial formulas for cluster variables of rank-two skew-symmetric cluster algebras. We identify a technical result that implies the bijection and make partial progress towards its proof. We then shift gears to study certain power series which arise as limits of ratios of …

Towards Tropical Psi Classes, Jawahar Madan

HMC Senior Theses

To help the interested reader get their initial bearings, I present a survey of prerequisite topics for understanding the budding field of tropical Gromov-Witten theory. These include the language and methods of enumerative geometry, an introduction to tropical geometry and its relation to classical geometry, an exposition of toric varieties and their correspondence to polyhedral fans, an intuitive picture of bundles and Euler classes, and finally an introduction to the moduli spaces of n-pointed stable rational curves and their tropical counterparts.

Exploring Winning Strategies For The Game Of Cycles, Kailee Lin

HMC Senior Theses

This report details my adventures exploring the Game of Cycles in search of winning strategies. I started by studying combinatorial game theory with hopes to use the Sprague-Grundy Theorem and the structure of Nimbers to gain insight for the Game of Cycles. In the second semester, I pivoted to studying specific types of boards instead. In this thesis I show that variations of the mirror-reverse strategy developed by Alvarado et al. in the original Game of Cycles paper can be used to win on additional game boards with special structure, such as lollipops, steering wheel locks, and 3-spoke trees. Additionally …

Modelling The Transition From Homogeneous To Columnar States In Locust Hopper Bands, Miguel Velez

HMC Senior Theses

Many biological systems form structured swarms, for instance in locusts, whose swarms are known as hopper bands. There is growing interest in applying mathematical models to understand the emergence and dynamics of these biological and social systems. We model the locusts of a hopper band as point particles interacting through repulsive and attractive social "forces" on a one dimensional periodic domain. The primary goal of this work is to modify this well studied modelling framework to be more biological by restricting repulsion to act locally between near neighbors, while attraction acts globally between all individuals. This is a biologically motivated …

On The Inverse Hull Of A One-Sided Shift Of Finite Type, Aria Beaupre

HMC Senior Theses

Let S be the semigroup constructed from a one-sided shift of finite type. In this thesis, we will provide the construction of H(S), the inverse hull of S, explore the properties of H(S), and begin to characterize the structure of H(S). We will also focus on a kind of one-sided shift of finite type, Markov shifts, and prove an invariant on isomorphic inverse hulls of Markov shifts.

Fractals, Fractional Derivatives, And Newton-Like Methods, Eleanor Byrnes

HMC Senior Theses

Inspired by the fractals generated by the discretizations of the Continuous Newton Method and the notion of a fractional derivative, we ask what it would mean if such a fractional derivative were to replace the derivatives in Newton's Method. This work, largely experimental in nature, examines these new iterative methods by generating their Julia sets, computing their fractal dimension, and in certain tractable cases examining the behaviors using tools from dynamical systems.

Temporal Coherent Control Of Resonant Two-Photon Double Ionization Of The Hydrogen Molecule Via Doubly Excited States, Jean Marcel Ngoko Djiokap, Anthony F. Starace

Anthony F. Starace Publications

We use time-delayed, counter-rotating, circularly polarized few-cycle attosecond nonoverlapping pulses to study the temporal coherent control of the resonant process of two-photon double ionization (TPDI) of hydrogen molecule via doubly excited states for pulse propagation direction along ˆk either parallel or perpendicular to the molecular axis ˆR. For ˆk ‖ ˆR and a pulse carrier frequency of 36 eV resonantly populating the Q₂ 1∏ ⁺ _u (1) doubly excited state as well as other 1∏ ⁺ _u doubly excited states, we find that the indirect ionization pathway through these doubly excited states changes the character of the kinematical vortex-shaped …

Recapture: A Virtual Reality Interactive Narrative Experience Concerning Perspectives And Self-Reflection, Indira Avendano

Honors Undergraduate Theses

This project presents a virtual reality (VR) Interactive Narrative aiming to leave users reflecting on the perspectives one chooses to view life through. The narrative is driven by interactions designed using the concept of procedural rhetoric, which explores how rules and mechanics in games can persuade people about an idea, and Shin's cognitive model, which presents a dynamic view of immersion in VR. The persuasive nature of procedural rhetoric in combination with immersion techniques such as tangible interfaces and first-person elements of VR can effectively work together to immerse users into a compelling narrative experience with an intended emotional response …

Molten Regolith Electrolysis Processing For Lunar Isru: Financial And Physics Analysis Of Spacex Starship Transportation, Cheyenne Harper

Honors Undergraduate Theses

The purpose of the following research is to explore molten regolith electrolysis (MRE) methodology for in-situ resource utilization (ISRU) of Highlands lunar regolith, to be explored during the initial Artemis missions. An analysis of potential commercial launch providers for MRE-equipment based on technology-readiness level (TRL), payload mass support, and $ USD/kg payload price is provided. SpaceX is ultimately proposed as a launch provider of MRE equipment following multi-factorial analysis, with the SpaceX Starship human landing system (HLS) variant proposed for supporting MRE payload. Finally, customers of regolith-derived oxygen, aluminum, and silicon are distinguished to form the business case for operating …

You Can't Lose A Game If You Don't Play The Game: Exploring The Ethics Of Gamification In Education, Dympna O'Sullivan, Ioannis Stavrakakis, Damian Gordon, Andrea Curley, Brendan Tierney, Emma Murphy, Michael Collins, Anna Becevel

Articles

Gamification has been hailed as a meaningful solution to the perennial challenge of sustaining student attention in class. It uses facets of gameplay in an educational context, including things such as points, leaderboards and badges. These are clearly efforts to make the student experience more entertaining and engaging, but nonetheless, they are also clearly digital nudges and attempts to change the students’ behaviours and attitudes to a specific set of concepts, and in which case they must, and should, be subject to the same ethical scrutiny as any other form of persuasion technique, as they may be unintentionally eroding the …

Best Cybersecurity Practices For Companies, Post Van Buren, Mary Riley

Cybersecurity Undergraduate Research Showcase

Imagine this scenario: you are a small business owner, and you’ve just been informed of a network security breach. In your Zoom meeting with the IT Department, you learned the details: network activity logs revealed aberrant behavior after hours. Threat actors accessed systems containing sensitive information and downloaded copies of key files containing company trade secrets, market strategies, and customer data – all within a matter of minutes. Immediately, you review the consequences of the breach in your mind: reputational harm, monetary loss, and potential lawsuits. You ask the IT professional about the root cause of the breach. Was it …

Predictive Maintenance Of Bearing Machinery Using Simulation- A Bibliometric Study, Karan Gulati Mr., Keshav Basandrai Mr., Shubham Tiwari Mr., Pooja Kamat Prof., Satish Kumar Dr.

Library Philosophy and Practice (e-journal)

Modelling is a way of constructing a virtual representation of software and hardware that involves a real-world device. We will discover the behaviour of the system if the software elements of this model are guided by mathematical relationships. For testing conditions that may be difficult to replicate with hardware prototypes alone, modelling and simulation are particularly useful, especially in the early phase of the design process when hardware might not be available. Model-based approach in MATLAB-Simulink can be useful for predictive maintenance of machines as it can reduce unplanned downtimes and maintenance costs when industrial equipment breaks. Through this bibliometric …

On The Usage And Vulnerabilities Of Api Systems, Conner D. Yu

Cybersecurity Undergraduate Research Showcase

To some, Application Programming Interface (API) is one of many buzzwords that seem to be blanketed in obscurity because not many people are overly familiar with this term. This obscurity is unfortunate, as APIs play a crucial role in today’s modern infrastructure by serving as one of the most fundamental communication methods for web services. Many businesses use APIs in some capacity, but one often overlooked aspect is cybersecurity. This aspect is most evident in the 2018 misuse case by Facebook, which led to the leakage of 50 million users’ records.1 During the 2018 Facebook data breach incident, threat actors …

Cybersecurity: Building A Better Defense With A Great Offense, David M. Cooke

Cybersecurity Undergraduate Research Showcase

The current industry standard for cybersecurity is risk mitigation, which is the identification, evaluation, and categorization of threats that are posed to an organization's network. The goal is to prevent attacks and if an organization is attacked popular standard is to react and remedy the attack. This form of cyber defense isn’t very reassuring to an organization and its users, once an attack is executed based on a study conducted by Booz Allen the average time an advanced persistent threat (APT) dwells on a victims’ network before it’s discovered is 200-250 days. That’s plenty of time for a malicious third …

Tackling Ai Bias With Gans, Noam Stanislawski

Cybersecurity Undergraduate Research Showcase

Throughout the relatively short history of artificial intelligence (AI), there has been a significant concern surrounding AI’s ability to incorporate and maintain certain characteristics which were not inherently modeled out in its coding. These behaviors stem from the prominent usage of neural network AI, which can inherit human biases from the input data it receives. This paper argues for two possible avenues to combat these biases. The first is to rethink the traditional framework for neural network projects and retool them to be usable by a Generative Adversarial Network (GAN). In a GAN’s zero-sum game, two network techniques can combat …

Structural Analysis And Interpretation Of Deformation Along The Keweenaw Fault System West Of Lake Gratiot, Keweenaw County, Michigan, Sophie A. Mueller

Dissertations, Master's Theses and Master's Reports

The Keweenaw fault is perhaps the most significant fault associated with the Midcontinent Rift System of the north-central United States. The fault, parallel to the south edge of the rift, has been interpreted as a rift-bounding normal fault that was inverted by subsequent compressional events, thrusting copper-bearing Portage Lake Volcanics (~ 1.1 Ga) over younger Jacobsville Sandstone. Geologic maps and cross sections published in the 1950s by the U. S. Geological Survey depict the fault with a well-defined, single, sinuous trace that is locally associated with smaller branch faults. Cross-sections from that time generally show a simple listric stratal geometry …

Quantifying The Value Of Foam-Based Flexible Floating Solar Photovoltaic Systems, Koami Soulemane Hayibo

Dissertations, Master's Theses and Master's Reports

Distributed generation with solar photovoltaic (PV) technology is economically competitive if net metered in the U.S. Yet there is evidence that net metering is misrepresenting the true value of distributed solar generation so that the value of solar (VOS) is becoming the preferred method for evaluating economics of grid-tied PV. VOS calculations are challenging and there is widespread disagreement in the literature on the methods and data needed. To overcome these limitations, this thesis reviews past VOS studies to develop a generalized model that considers realistic future avoided costs and liabilities. The approach used here is bottom-up modeling where the …

Impact Of Hemodynamic Vortex Spatial And Temporal Characteristics On Analysis Of Intracranial Aneurysms, Kevin W. Sunderland

Dissertations, Master's Theses and Master's Reports

Subarachnoid hemorrhage is a potentially devastating pathological condition in which bleeding occurs into the space surrounding the brain. One of the prominent sources of subarachnoid hemorrhage are intracranial aneurysms (IA): degenerative, irregular expansions of area(s) of the cerebral vasculature. In the event of IA rupture, the resultant subarachnoid hemorrhage ends in patient mortality occurring in ~50% of cases, with survivors enduring significant neurological damage with physical or cognitive impairment. The seriousness of IA rupture drives a degree of clinical interest in understanding these conditions that promote both the development and possible rupture of the vascular malformations. Current metrics for the …

Explainable Feature- And Decision-Level Fusion, Siva Krishna Kakula

Dissertations, Master's Theses and Master's Reports

Information fusion is the process of aggregating knowledge from multiple data sources to produce more consistent, accurate, and useful information than any one individual source can provide. In general, there are three primary sources of data/information: humans, algorithms, and sensors. Typically, objective data---e.g., measurements---arise from sensors. Using these data sources, applications such as computer vision and remote sensing have long been applying fusion at different "levels" (signal, feature, decision, etc.). Furthermore, the daily advancement in engineering technologies like smart cars, which operate in complex and dynamic environments using multiple sensors, are raising both the demand for and complexity of fusion. …

Superresolution Enhancement With Active Convolved Illumination, Anindya Ghoshroy

Dissertations, Master's Theses and Master's Reports

The first two decades of the 21st century witnessed the emergence of “metamaterials”. The prospect of unrestricted control over light-matter interactions was a major contributing factor leading to the realization of new technologies and advancement of existing ones. While the field certainly does not lack innovative applications, widespread commercial deployment may still be several decades away. Fabrication of sophisticated 3d micro and nano structures, specially for telecommunications and optical frequencies will require a significant advancement of current technologies. More importantly, the effects of absorption and scattering losses will require a robust solution since this renders any conceivable application of metamaterials …

Understanding The Effects Of Water Vapor And Temperature On Aerosol Using Novel Measurement Methods, Tyler Jacob Capek

Dissertations, Master's Theses and Master's Reports

Aerosol and water are inexorably linked, and both are ubiquitous within our atmosphere and required components for cloud formation. Relative humidity (RH), a temperature dependent quantity, can have a significant influence on the size, shape, and ultimately, the optical properties of the aerosol. RH can vary substantially on small spatial and short temporal scales in turbulent conditions due to rapid fluctuations in temperature and water vapor mixing ratio. Accurate assessment of optical enhancements due to an increase in RH is key for determining the particles’ impact on the climate and visibility.

A humidity-controlled cavity attenuated phase-shift albedometer (H-CAPS-PM_SSA) …

Volcan De Fuego: A Machine Learning Approach In Understanding The Eruptive Cycles Using Precursory Tilt Signals, Kay Sivaraj

Dissertations, Master's Theses and Master's Reports

Volcan de Fuego is an active stratovolcano located in the Central Guatemalan segment of the 1100 m long Central America Volcanic Arc System (CAVAS). Fuego-Acatenango massif consists of at least four major vents of which the Fuego summit vent is the most active and the youngest member. The volcano exhibits primarily Strombolian and Vulcanian behavior along with occasional paroxysms and pyroclastic flows. Historically, Fuego has produced basaltic-andesitic rocks with more recent eruptions progressively trending towards maficity. Several studies have used short-term deployments of broadband seismometers, infrasound, and long-term remote sensing techniques to characterize the mechanism of Fuego. In our study, …

Improving The Temporal Accuracy Of Turbulence Models And Resolving The Implementation Issues Of Fluid Flow Modeling, Kyle J. Schwiebert

Dissertations, Master's Theses and Master's Reports

A sizeable proportion of the work in this thesis focuses on a new turbulence model, dubbed ADC (the approximate deconvolution model with defect correction). The ADC is improved upon using spectral deferred correction, a means of constructing a higher order ODE solver. Since both the ADC and SDC are based on a predictor-corrector approach, SDC is incorporated with essentially no additional computational cost. We will show theoretically and using numerical tests that the new scheme is indeed higher order in time than the original, and that the benefits of defect correction, on which the ADC is based, are preserved.

The …

Determination Of Molecular Markers Of Vaccinium Berry Standard Reference Materials Through Differential Analysis With Ultrahigh Resolution Lc/Ms, Abby Mikolitis

Dissertations, Master's Theses and Master's Reports

Blueberries and cranberries have vastly different flavor profiles despite both being a part of the Vaccinium genus. Their high content of phenolics makes them subjects of interest in preventative medicine, especially research in illnesses such as heart disease and cancer. Analysis has primarily focused on the identification and characterization of polyphenols, primarily anthocyanins which are a subclass of polyphenols, with ultra-high performance liquid chromatography coupled with electrospray ionization high resolution mass spectrometry (UHPLC-ES/HRMS). This study aims to develop a novel method of non-targeted UHPLC-ES/MS analysis with post processing and formula assignment performed with MZmine 2.53 and MFAssignR software tools. Pairing …

New Numerical Approximations Of Geological Processes In Heterogeneous Systems Using Radial Basis Functions, Nadun Lakshitha Dissanayake Kulasekera Mudiyanselage

Dissertations, Master's Theses and Master's Reports

This dissertation includes four chapters. A brief description of each chapter is organized as follows. The first chapter provides an introduction to the RBF method. The chapter follows the historical progression of the Radial Basis Function (RBF) method while outlining the method’s advantages and disadvantages. A brief introduction about RBF interpolation, the RBF-FD method, and how to use it to solve PDEs is provided. Chapter 2 introduces a novel computationally efficient RBF-FD algorithm to solve the groundwater flow equation in the presence of an active well. We show that our method analytically handles the singularities in the PDE caused by …

Statistical Methods In Genetic Studies, Cheng Gao

Dissertations, Master's Theses and Master's Reports

This dissertation includes three Chapters. A brief description of each chapter is organized as follows.

In Chapter 1, we proposed a new method, called MF-TOWmuT, for genome-wide association studies with multiple genetic variants and multiple phenotypes using family samples. MF-TOWmuT uses kinship matrix to account for sample relatedness. It is worth mentioning that in simulations, we considered hidden polygenic effects and varied the proportion of variance contributed by it to generate phenotypes. Simulation studies show that MF-TOWmuT can preserve the type I error rates and is more powerful than several existing methods in different simulation scenarios, MFTOWmuT is also quite …

A Methodology For The Creation Of Volcanic Gas Hazard Maps Using Satellite-Derived Sulfur Dioxide, Sanna J. Mairet

Dissertations, Master's Theses and Master's Reports

Sulfur dioxide (SO₂) gas has been shown to be detrimental to human and environmental health and is emitted continuously from anthropogenic and volcanic sources. Sulfur dioxide is the main target gas used for the detection of hazardous volcanic plumes due to its ease of detection by satellite sensors. However, quantitative information on potential ground-level exposure to volcanic SO₂ (i.e., a volcanic gas ‘hazard map’) is currently unavailable for the vast majority of active volcanoes. Utilizing sulfur dioxide vertical column densities retrieved from the Ozone Monitoring Instrument on NASA’s Aura satellite, Gridded Population of the World v.4, planetary …

Utilization Of Paenibacillus Polymyxa In The Recovery Of Lithium Bearing Minerals, Diana Bullen

Dissertations, Master's Theses and Master's Reports

In the global transition to green energy in the transportation and power production sectors, lithium has emerged as a viable solution, and crucial component, for the effective storage of renewable resources. To avoid further degradation of the land due to mining for virgin material, methods focused on recovering lithium must be developed. This research project seeks to explore a new way to recover lithium by using the bacterium Paenibacillus polymyxa. The bacteria were grown and then applied to the lithium bearing mineral spodumene. Settling velocity profiles were constructed for different treatments of spodumene. It was found that the spodumene …