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Social Media Is A Juggernaut: Lagged Correlation Analysis Using Ngram Data On “Internet” And “Social Media” With Amplification By The Advent Of The “Iphone”, William Zywiak, Gao Niu, Nicolas Petrell, Victoria Nichele, Kirsten Hokeness Jun 2026

Social Media Is A Juggernaut: Lagged Correlation Analysis Using Ngram Data On “Internet” And “Social Media” With Amplification By The Advent Of The “Iphone”, William Zywiak, Gao Niu, Nicolas Petrell, Victoria Nichele, Kirsten Hokeness

Mathematics and Economics Faculty Journal Articles

The amount of new information transmitted per day can be overwhelming. The data available through Ngram Viewer allows statistical examination to determine the most salient topics, as well as lagged correlation and lagged variance to support possible causal connections between concepts. Using this database, we determined that COVID, crypto, microplastics, and especially social media are important topics of the last few years. We also present results that suggest the development of the internet and the iPhone fueled the prominence of social media, and the access of the iPhone also increased access to the internet.


Fairlinked: Data Fairification Tools For Materials Data Science, Van D. Tran, Brandon Lee, Ritika Lamba, Henry Dirks, Quynh D. Tran, Balashanmuga Priyan Rajamohan, Ozan Dernek, Laura S. Bruckman, Yinghui Wu, Erika I. Barcelos, Roger H. French Jun 2026

Fairlinked: Data Fairification Tools For Materials Data Science, Van D. Tran, Brandon Lee, Ritika Lamba, Henry Dirks, Quynh D. Tran, Balashanmuga Priyan Rajamohan, Ozan Dernek, Laura S. Bruckman, Yinghui Wu, Erika I. Barcelos, Roger H. French

Student Scholarship

FAIRLinked is a software package created to support the FAIRification of materials science data, ensuring proper alignment with FAIR principles: Findable, Accessible, Interoperable, and Reusable. It is built to be compatible with MDS-Onto, an ontology designed to capture the semantics of various types of materials data, enabling integration and sharing across different research workflows. The package is subdivided into three subpackages: InterfaceMDS, RDFTableConversion, and QBWorkflow. The first subpackage, InterfaceMDS allows users to search for terms using either string search or various filters, explore different domains and subdomains, and add terms to MDS-Onto. RDFTableConversion is used for serialization and deserialization of …


3dcotton, Md Ahmed Al Muzaddid, William J. Beksi Jun 2026

3dcotton, Md Ahmed Al Muzaddid, William J. Beksi

Agriculture - Archive

3DCotton is an image dataset consisting of 8 cotton plants recorded at the Texas A&M University Research Farm. The images were captured using an Apple iPhone at a resolution of 1040x1920 pixels. Approximately 150 images per plant were taken from a distance of 1 m by recording multiple viewpoints. These images can be utilized for developing 3D reconstruction methods.


Ms110 Syllabus: Introduction To Computers, Information Systems, And Artificial Intelligence, Wei Zhang Jun 2026

Ms110 Syllabus: Introduction To Computers, Information Systems, And Artificial Intelligence, Wei Zhang

Management Science and Information Systems Faculty Publication Series

This is a syllabus for Professor Wei Zhang's MS110: Introduction to Computers, Information Systems and Artificial Intelligence Course within UMass Boston's College of Management. This is an Open Educational Resource and can be remixed, copied, redistributed, altered and reused as long as permission is given to the original creator.


Radiotheranostics For Gynecological Pathologies, Joni Sebastiano Jun 2026

Radiotheranostics For Gynecological Pathologies, Joni Sebastiano

Dissertations, Theses, and Capstone Projects

Molecular imaging, specifically positron emission tomography (PET), is vital for detecting disease and understanding its biological makeup. The exploitation of radiolabeled antibodies for PET imaging has proven to be indispensable to the field of molecular imaging over the last several decades. The development of radioimmunoconjugates for use in immunoPET has not only allowed for the sensitive, specific, and high-resolution detection of disease, but has also enabled a deeper understanding of the disease biology, ultimately guiding more personalized therapeutic strategies. Most typically, this technology is harnessed for the diagnosis and treatment of cancer, however more recently, the field has explored the …


Mediating Energy And Charge Transfer Dynamics Of Lead Halide Perovskite Nanocrystals Via Surface Chemical Approaches, Aaron S. Malinoski Jun 2026

Mediating Energy And Charge Transfer Dynamics Of Lead Halide Perovskite Nanocrystals Via Surface Chemical Approaches, Aaron S. Malinoski

Dissertations, Theses, and Capstone Projects

Energy and charge transfer are the fundamental mechanisms by which semiconductor nanocrystals interact with their external environment and underpin all light-conversion related applications. Lead halide perovskite nanocrystals (PNCs) are a relatively new class of semiconductor nanocrystals that possess a unique and dynamic surface chemical environment. Investigations into the influence of these surface chemical conditions on the electronic coupling between surface-bound molecular acceptors and the perovskite nanocrystals, and how the surface chemistry can be manipulated, in turn controlling the charge and energy transfer mechanisms, is the focus of this dissertation. Through ligand-shell engineering using commercially available, inexpensive small molecules, the surface …


Algorithmic Problems In Automorphic Orbits Of Free Groups, Siobhan B. O'Connor Jun 2026

Algorithmic Problems In Automorphic Orbits Of Free Groups, Siobhan B. O'Connor

Dissertations, Theses, and Capstone Projects

One of the fundamental problems in the field of combinatorial group theory is telling when two group presentations represent isomorphic groups. Since applying a free group automorphism to the set of relators of a presentation gives an isomorphic group, we want to be able to quickly decide when looking at a relator whether a given word can be sent to it via an automorphism. We give a hands-on introduction to the automorphisms of free groups using patterns of colored beads. We show that you can make this decision correctly in constant time on average by looking for "orbit-blocking" words that …


Electromagnetic Counterparts To Active Galactic Nucleus Disk-Embedded Binary Black Hole Mergers, Emily Mcpike Jun 2026

Electromagnetic Counterparts To Active Galactic Nucleus Disk-Embedded Binary Black Hole Mergers, Emily Mcpike

Dissertations, Theses, and Capstone Projects

The accretion disks of active galactic nuclei (AGN) are promising environments for producing binary black hole (BBH) mergers, which have been detected via gravitational waves (GW) with LIGO-Virgo-KAGRA (LVK). BBH mergers embedded in AGN disks are unique among GW formation channels in their generic ability to produce electromagnetic (EM) counterparts, via interactions between the merger remnant and the surrounding disk gas (though these are not always observable). While such mergers represent valuable multi-messenger sources, the lack of predictive statistical models in existing literature currently limits our ability to select possible EM counterparts with GW detections in archival data and in …


Variational Methods For Semilinear Pdes With Dirac Singularities, Samuel J. Magill Jun 2026

Variational Methods For Semilinear Pdes With Dirac Singularities, Samuel J. Magill

Dissertations, Theses, and Capstone Projects

This dissertation utilizes a variational framework for semilinear elliptic equations in two dimensions with Dirac measure data. The central objects of study are equations of the form −ΔU = f(U) + Σj=1N αjδpj on bounded Lipschitz domains Ω ⊂ ℝ² with homogeneous Dirichlet boundary condition, and on a flat torus 𝕋², where αj is positive for the Dirichlet setting and αj is negative on the torus. Solutions are obtained by minimizing the restriction of an energy functional to an order interval determined by explicit sub- and supersolutions; the Euler–Lagrange equation is recovered …


Considering Numerical Relativity For Upgrades In Mcfacts Merger Dynamics, Shawn K. Ray Jun 2026

Considering Numerical Relativity For Upgrades In Mcfacts Merger Dynamics, Shawn K. Ray

Dissertations, Theses, and Capstone Projects

Binary black hole mergers (BBH), some likely originating from active galactic nuclei (AGN), are observed by ground-based detectors such as LIGO-Virgo-KAGRA (LVK) and will be detected by future space-based detectors such as the Laser Interferometer Space Antenna (LISA) and the Laser Interferometer Lunar Antenna (LILA). The dynamics of AGN may be responsible for a significant fraction of BBH mergers soon to be observed by LISA and LILA, yet the dynamics of BBH mergers within AGN disks remains ambiguous despite their appearance in gravitational wave observations. Monte carlo For AGN Channel Testing and Simulation (McFACTS) is an open-source software used to …


Inductive Biases In Field-Level Cosmological Inference From Galaxy Catalogs, James O'Connor Baldwin Jun 2026

Inductive Biases In Field-Level Cosmological Inference From Galaxy Catalogs, James O'Connor Baldwin

Dissertations, Theses, and Capstone Projects

We perform field-level likelihood-free inference of the matter density parameter Ωm from simulated galaxy catalogs using machine learning models with differing inductive biases. Using features extracted from hydrodynamic simulations in the CAMELS suite, we investigate how both observable choice and model architecture govern the extraction of cosmological information. We consider galaxy positions and line-of-sight peculiar velocities, both separately and in combination, and compare permutation-invariant Deep Sets, implemented with either standard multilayer perceptrons (MLPs) or Kolmogorov–Arnold Networks (KANs), to graph neural networks (GNNs) implemented with MLPs, which explicitly encode spatial relations. We evaluate inference performance under both in-distribution and out-of-distribution (OOD) …


Reexamining The Croton Aqueduct: A Ward-Level Microhistorical Analysis Of Infrastructure And Cholera Mortality In 1849 New York City, Alexandria R. Toothman Jun 2026

Reexamining The Croton Aqueduct: A Ward-Level Microhistorical Analysis Of Infrastructure And Cholera Mortality In 1849 New York City, Alexandria R. Toothman

Dissertations, Theses, and Capstone Projects

This work reexamines the Croton Aqueduct’s role in public health by shifting analysis from the citywide level to the ward level, revealing that infrastructure expansion did not produce uniform benefits across New York City. When the Croton Aqueduct opened in 1842, it was celebrated as an achievement that would deliver pure water and eliminate disease. However, only seven years after its opening, in 1849, cholera returned with greater force in the Sixth Ward. This work shows that the uneven distribution of Croton infrastructure corresponded with uneven cholera mortality rates, challenging narratives that present Croton as a singular triumph of urban …


Identifying Textual Predictors Of Early Termination In Clinical Trials In Medicine: An Explainable Machine-Learning Study, Rohan Ramnarain Jun 2026

Identifying Textual Predictors Of Early Termination In Clinical Trials In Medicine: An Explainable Machine-Learning Study, Rohan Ramnarain

Dissertations, Theses, and Capstone Projects

About one in five clinical trials in medicine ends early, wasting valuable resources and reducing the evidence available for developing life-saving medical treatments. This project uses a method called Trial2Vec, which is a self-supervised machine-learning method that converts clinical trial documents into dense numerical representations that capture their key design and clinical characteristics, to turn each proposed clinical trial’s written protocol into a compact numerical profile (a process referred to as embedding). These profiles are then paired with a predictive machine learning models to identify the words and phrases in the trial documents that can signal a higher risk of …


Discovery Of Newly Resolved Filament And Extraplanar Gas In M33 With The Local Group L-Band Survey, Emma Taylor Kleiner Jun 2026

Discovery Of Newly Resolved Filament And Extraplanar Gas In M33 With The Local Group L-Band Survey, Emma Taylor Kleiner

Dissertations, Theses, and Capstone Projects

The proximity of the Local Group allows for unparalleled resolution of the structure and kinematics of the ISM while simultaneously observing the overall rotation of the galaxy. These nearby galaxies present the opportunity to probe stellar feedback processes in various galactic environments. M33 in particular, offers insight into the nature of the extended neutral gas and its relationship with the star-forming disk and the surrounding CGM, by way of its classic star-forming spiral and relatively undisturbed system. Outside of M33’s distinguished warp, the galaxy offers little evidence of satellites and shows few signs of interaction, begging the question of how …


Ppg-Sport: A Dataset For Reliable Heart Rate Monitoring From Wrist Ppg Under Dynamic Sports Conditions, Changshuo Hu, Hung Manh Pham, Yiming Zhang, Guanru Yan, Xiao Ma, Yuezhong Wu, Thivya Kandappu, Archan Misra, Dong Ma Jun 2026

Ppg-Sport: A Dataset For Reliable Heart Rate Monitoring From Wrist Ppg Under Dynamic Sports Conditions, Changshuo Hu, Hung Manh Pham, Yiming Zhang, Guanru Yan, Xiao Ma, Yuezhong Wu, Thivya Kandappu, Archan Misra, Dong Ma

Research Collection School Of Computing and Information Systems

Photoplethysmography (PPG) has become a cornerstone of physiological sensing in wearable devices, enabling non-invasive monitoring of heart rate and related biomarkers. However, its reliability deteriorates sharply under dynamic, high-intensity, or non-periodic motions such as those in sports, where existing datasets fail to capture realistic wrist dynamics. To address this gap, we introduce PPG-Sport, the first large-scale dataset designed for heart rate monitoring from wrist-worn PPG under real sports conditions. The PPG-Sport dataset includes synchronized PPG, inertial measurement unit (IMU), and electrocardiography (ECG) recordings from both wrists of 30 participants across six representative activities: stationary, walking, running, badminton, table tennis, and …


Phases And Dynamics Of An Impurity Immersed In One-Dimensional Quantum Droplets, Dimitrios Diplaris, Ilias A. Englezos, Friethjof Theel, Peter Schmelcher, Simeon I. Mistakidis Jun 2026

Phases And Dynamics Of An Impurity Immersed In One-Dimensional Quantum Droplets, Dimitrios Diplaris, Ilias A. Englezos, Friethjof Theel, Peter Schmelcher, Simeon I. Mistakidis

Physics Faculty Research & Creative Works

We explore the ground-state properties of a single impurity immersed in a one-dimensional quantum droplet medium formed by a two-component Bose mixture. Relying on ab initio simulations, we demonstrate that tuning the impurity–droplet interactions allows to controllably reshape the droplets' density profiles and associated correlation patterns. For attractive impurity-medium couplings, the impurity becomes localized within the droplet, which exhibits a density hump at the vicinity of the impurity, while repulsive interactions facilitate phase separation. Comparing our many-body results with the appropriate extended Gross–Pitaevskii description, we find adequate agreement for the droplet density profiles, with the effective field approach systematically overestimating …


Emotional Support Through Ai: Venting To Artificial Intelligence Or A Perceived Human May Offer Comparable Emotional Well-Being Benefits, Meilan Hu, Jerlyn Q. H. Ho, Claire Ng, Shermaine S. M. Wong, Andree Hartanto Jun 2026

Emotional Support Through Ai: Venting To Artificial Intelligence Or A Perceived Human May Offer Comparable Emotional Well-Being Benefits, Meilan Hu, Jerlyn Q. H. Ho, Claire Ng, Shermaine S. M. Wong, Andree Hartanto

Research Collection School of Social Sciences

Artificial Intelligence (AI) chatbots are increasingly being explored as sources of informal emotional support, with emerging evidence suggesting that venting to these systems can reduce negative affect. Yet, it remains unclear whether such benefits depend on the responder's perceived identity. Given that emotional relief from venting often hinges on perceived authenticity and emotional validation, this study investigates whether the emotional well-being benefits of venting differ when users believe they are interacting with an AI chatbot versus a human, even when responses are content-matched. In a pre-registered experiment ( N = 279), participants were randomly assigned to either an AI-assisted venting …


“From Remembering To Shaping”: Narrating Shared Experiences By Co-Designing Cultural Heritage Artifacts In Collaborative Vr, Yushang Yang, Fanxu Meng, Fiona Fui-Hoon Nah, L. C. Ray Jun 2026

“From Remembering To Shaping”: Narrating Shared Experiences By Co-Designing Cultural Heritage Artifacts In Collaborative Vr, Yushang Yang, Fanxu Meng, Fiona Fui-Hoon Nah, L. C. Ray

Research Collection School Of Computing and Information Systems

The ways people remember and recall places reveal an invisible aspect of cultural heritage (CH), reflecting how individuals and communities relate to these places. Heritage is communal, emerging through collaboratively constructed narratives rather than individual records. To probe how people may share collective memories, we designed an immersive two-person workflow for collaboratively co-designing 3D artifacts and environments in virtual heritage locations, using Generative AI (GenAI) to instantiate these intangible memories. Observations of the co-creation process revealed that participants merged prompts and model placements when negotiating different perspectives. They used spatial operations to compose scenes, and also to express personal and …


Context Matters: Auditing Gender Bias In T2i Generation Through Risk-Tiered Use-Case Profiles, Jose Luis Luna Campoverde, Yankun Wu, Xiaofei Xie, Noa Garcia Jun 2026

Context Matters: Auditing Gender Bias In T2i Generation Through Risk-Tiered Use-Case Profiles, Jose Luis Luna Campoverde, Yankun Wu, Xiaofei Xie, Noa Garcia

Research Collection School Of Computing and Information Systems

Text-to-image (T2I) generative models are increasingly used to produce content for education, media, and public-facing communication, and are starting to be integrated into higher-impact pipelines. Since generated images tend to reinforce stereotypes, producing representational erasure via “default” depictions and shaping perceptions of who belongs in certain roles, a growing body of work has proposed metrics to quantify gender bias in T2I outputs. Yet existing evaluations remain fragmented. Metrics are often reported without a shared view of what they measure, what assumptions they entail, or how their results should be interpreted under different deployment contexts. This limits the usefulness of gender …


Parkinson’S Disease Phenotype Stratification Using Multiple Correspondence Analysis, Kelly Astudillo Jun 2026

Parkinson’S Disease Phenotype Stratification Using Multiple Correspondence Analysis, Kelly Astudillo

Dissertations, Theses, and Capstone Projects

Parkinson’s disease (PD) is the second most common neurodegenerative disorder, with over 12 million people projected to be affected by 2040 (Dorsey et al., 2018). Deep phenotyping and stratification can provide useful information regarding PD pathogenesis and can aid in the  development of disease modifying therapies that aim to delay the progression or prevent the onset of neurodegeneration (Blandini et al., 2019; Smith & Schapira, 2022). Utilizing multivariate methods such as multiple correspondence analysis (MCA) permits for the simultaneous analysis of distinct data modalities. To the best of our knowledge, MCA has not been previously used to explore phenotype patterns …


A Predictive Coding Account Of Spatial Working Memory Following Prophylactic Levetiracetam Administration Prior To Traumatic Brain Injury, Omeima Mutwali Jun 2026

A Predictive Coding Account Of Spatial Working Memory Following Prophylactic Levetiracetam Administration Prior To Traumatic Brain Injury, Omeima Mutwali

Dissertations, Theses, and Capstone Projects

Traumatic brain injury (TBI) symptom prevention and remediation is an important area of research that would benefit vulnerable groups, including active-duty and veteran soldiers. These patients can sustain penetrative forces in fields of combat or in training, which result in focal lesions that trigger inflammatory and degenerative processes in the brain. Both primary and secondary injuries are associated with changes to cognition, behavior and affective state. This disease poses increased risk of epileptogenesis, as well. Given these outcomes, prior research has evaluated levetiracetam (LEV) as a prophylactic treatment for seizures, cognitive deficits and negative emotionality. LEV acts as a presynaptic …


1d Crust-Magnetosphere Coupling Model For Magnetars, Kennedy M. Jeter Jun 2026

1d Crust-Magnetosphere Coupling Model For Magnetars, Kennedy M. Jeter

Dissertations, Theses, and Capstone Projects

Magnetars are the most extremely magnetized objects in the universe. Their strong magnetic fields generate high-energy magnetic flares with instantaneous luminosity that can outshine their host galaxy. Previous works have explored how Hall drift in the crust affects the dynamics of magnetic field lines in the magnetosphere. This work investigates how a change in the magnetosphere, such as a flare or an outburst, can excite Hall evolution in the crust. We investigate how the twisting and untwisting of magnetic field lines in a magnetar’s magnetosphere launches Hall waves through its crust using a one-dimensional numerical model. We use the Dedalus …


Whitney Extension Problem For Fractional Sobolev Spaces And Besov Spaces, Han Li Jun 2026

Whitney Extension Problem For Fractional Sobolev Spaces And Besov Spaces, Han Li

Dissertations, Theses, and Capstone Projects

In the dissertation, we go through the development of the Whitney extension problem and prove a type of results for the Whitney extension problem for homogeneous fractional Sobolev spaces and homogeneous Besov spaces.

This dissertation consists of four chapters:

Chapter 1: We recall the history of the Whitney extension problem and talk about some early works which have been done for the Whitney extension problem. We also mention our new results.

Chapter 2: We introduce some basic notations, definitions and preliminary results.

Chapter 3: We show the existence of a bounded linear extension operator for homogeneous fractional Sobolev space L …


Supramolecular Assembly In Short Peptide Systems For Selective Metabolite Recognition And Drug Nanoencapsulation, Maithreyi Ramakrishnan Jun 2026

Supramolecular Assembly In Short Peptide Systems For Selective Metabolite Recognition And Drug Nanoencapsulation, Maithreyi Ramakrishnan

Dissertations, Theses, and Capstone Projects

Short peptides can form adaptive supramolecular assemblies, and understanding how minimal sequences organize around neurometabolites or hydrophobic cancer drugs enables the rational design of functional materials. This thesis combines molecular dynamics with experimental validation to establish design rules linking peptide sequence to emergent structure and function. Chapter 1 outlines the molecular determinants governing peptide assembly. Chapter 2 reviews computational workflows that reveal sequence-dependent conformations and supramolecular organization. Chapter 3 applies these principles to Dynamic Peptide Libraries which identify tetrapeptides that selectively interact with neurometabolites. Chapter 4 extends the same interaction-driven framework to design tryptophan-rich pentapeptides that co-assemble with kinase inhibitors …


Quiver Of Affine Monoid Of A Vector Space Over Finite Field, James Junie Chen Cleary Jun 2026

Quiver Of Affine Monoid Of A Vector Space Over Finite Field, James Junie Chen Cleary

Dissertations, Theses, and Capstone Projects

In this paper, we study the quiver of the complex monoid algebra CAFF(n, q). There are n + 1 maximal subgroups of AFF(n, q), each isomorphic to AGL(k, q) for some 0 ≤ k ≤ n. Every irreducible representation of CAFF(n, q) arises from a character of CAGL(k, q) for a suitable k. Thus, we study two different approaches to classifying the characters of CAGL(k, q). Next, we compute the full quiver Q(CAFF(n, q)). Finally, we show that this quiver is a disjoint union of straight-line paths and that its basic algebra has radical square zero. Hence, it has finite …


Computational Insights Into Nucleosome Dynamics In Epigenetics Using Molecular Dynamics Simulations, Rutika Patel Jun 2026

Computational Insights Into Nucleosome Dynamics In Epigenetics Using Molecular Dynamics Simulations, Rutika Patel

Dissertations, Theses, and Capstone Projects

Nucleosome core particles (NCP) are the building blocks that form a highly organized and compact chromatin structure. Nucleosomes package DNA in the nucleus of eukaryotic cells. The NCP consists of about 147 base pairs of DNA wrapped around the histone octamer, with 1.65 superhelical turns in a left-handed manner. The histone octamer is composed of two copies of H3, H4, H2A, and H2B. Together with histone H1 and linker DNA, they further assemble into a higher-order chromatin structure. The nucleosome complex is stabilized by electrostatic interactions between positively charged histone residues and the negatively charged DNA backbone. To effectively access …


Scaling Limits Of Critical Observables Through The High Dimensional Incipient Infinite Cluster, Pranav Chinmay Jun 2026

Scaling Limits Of Critical Observables Through The High Dimensional Incipient Infinite Cluster, Pranav Chinmay

Dissertations, Theses, and Capstone Projects

We give a general construction of the incipient infinite cluster in high dimensional percolation, and use it as a decoupling tool to rigorize geometric heuristics for analyzing the asymptotics of observables at criticality. Examples include demonstrating the limiting distribution of the chemical distance and full-strength asymptotics for k-point functions, which constitute foundational inputs for scaling limit results associated to critical clusters.


Navigating Oer Support Without Drowning In Ai, Lydia Burrage-Goodwin, Christine Moynihan Jun 2026

Navigating Oer Support Without Drowning In Ai, Lydia Burrage-Goodwin, Christine Moynihan

Joseph P. Healey Library Publications

This was a presentation at the June 2026 Boston Library Consortium at Connecticut College.

UMB Healey Librarians Lydia Burrage-Goodwin and Christine Moynihan talk about what experiences they have had with faculty using OER and AI, which led them to develop ethics guidelines to support librarians who work with faculty authors. Attendees learned about creating AI use statements for OERs, using AI transparency logos, and applying open licenses to fully AI generated content as well as OER adaptations.


Modeling Turbulent Accretion Flows Around Black Holes: Azimuthal Flux Derivative Density Curves In 3d Mhd Simulations, Sasmitha Purushothaman, Matthew D. Duez, Pavan Chawhan Jun 2026

Modeling Turbulent Accretion Flows Around Black Holes: Azimuthal Flux Derivative Density Curves In 3d Mhd Simulations, Sasmitha Purushothaman, Matthew D. Duez, Pavan Chawhan

University Honors Theses

When modeling two-dimensional axisymmetric accretion disks around Kerr black holes, setting the azimuthal terms of the MHD equations to zero causes the loss of turbulence and dynamo effects. In this paper, we use three-dimensional models to identify the turbulence that arises from azimuthal flux derivatives (AFDs) and create probability density functions to characterize them. We establish a pipeline for calculating the AFDs, creating a distribution, and normalizing it. Then, we plot the dependence of the conditional probability of the AFDs on density, magnetic field strength, and velocity for the continuity and magnetic induction equations. Future research can take this information …


Comparing The Sensitivity And Degree Of Boolean Functions Via The Hypercube, Anne-Caroline Rupp Jun 2026

Comparing The Sensitivity And Degree Of Boolean Functions Via The Hypercube, Anne-Caroline Rupp

University Honors Theses

This thesis studies three complexity measures of total Boolean functions f:{0,1}n → {0,1}: maximum sensitivity s(f), polynomial degree deg(f), and spectral sensitivity λ(f), where λ(f) is defined as the spectral norm of the adjacency matrix of the sensitivity graph. Building on the results of Aaronson et al., we examine the inequality chain √s(f) ≤ λ(f) ≤ deg(f) and investigate whether all three quantities can be simultaneously equal.

The first part of the thesis reverse engineers the equality cases of the two known inequalities to isolate necessary extremal conditions on both the Fourier structure of f and the local geometry …