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On The Improved Convergence Of Lifted Distributional Gauss Curvature From Regge Elements, Jay Gopalakrishnan, Michael Neunteufel, Joachim Schöberl, Max Wardetzky Nov 2024

On The Improved Convergence Of Lifted Distributional Gauss Curvature From Regge Elements, Jay Gopalakrishnan, Michael Neunteufel, Joachim Schöberl, Max Wardetzky

Mathematics and Statistics Faculty Publications and Presentations

Although Regge finite element functions are not continuous, useful generalizations of nonlinear derivatives like the curvature, can be defined using them. This paper is devoted to studying the convergence of the finite element lifting of a generalized (distributional) Gauss curvature defined using a metric tensor approximation in the Regge finite element space. Specifically, we investigate the interplay between the polynomial degree of the curvature lifting by Lagrange elements and the degree of the metric tensor in the Regge finite element space. Previously, a superconvergence result, where convergence rate of one order higher than expected, was obtained when the approximate metric …


A 3d Memristor Architecture For In-Memory Computing Demonstrated With Sha3, Muayad J. Aljafar, Rasika Joshi, John M. Acken Nov 2024

A 3d Memristor Architecture For In-Memory Computing Demonstrated With Sha3, Muayad J. Aljafar, Rasika Joshi, John M. Acken

Electrical and Computer Engineering Faculty Publications and Presentations

Security is a growing problem that needs hardware support. Memristors provide an alternative technology for hardware-supported security implementation. This paper presents a specific technique that utilizes the benefits of hybrid CMOS-memristors technology demonstrated with SHA3 over implementations that use only memristor technology. In the proposed technique, SHA3 is implemented in a set of perpendicular crossbar arrays structured to facilitate logic implementation and circular bit rotation (Rho operation), which is perhaps the most complex operation in SHA3 when carried out in memristor arrays. The Rho operation itself is implemented with CMOS multiplexers (MUXs). The proposed accelerator is standby power-free and circumvents …


The Universal And The Unique, Martin Zwick Nov 2024

The Universal And The Unique, Martin Zwick

Complex Systems Faculty Publications and Presentations

This paper explores the abstract dyad of universality and uniqueness. It notes that the two might be complementary and even synergistic, or that they might be alternatives that oppose one another. It also explores how the unique might be an emergent from a primal universality, as well as how the universal might be an emergent from a primal uniqueness. Finally, it offers an interpretation of this dyad in which the universal and the unique are equivalent transforms of one another and thus two sides of the same coin.

Keywords: Universality, uniqueness, general and particular, similarity and difference, fundamental dyad, dualism


A Finite-Horizon Approach To Active Level Set Estimation, Phillip Kearns, Bruno Jedynak, John Lipor Nov 2024

A Finite-Horizon Approach To Active Level Set Estimation, Phillip Kearns, Bruno Jedynak, John Lipor

Mathematics and Statistics Faculty Publications and Presentations

We consider the problem of active learning for level set estimation (LSE), where the goal is to localize all regions where a function of interest lies above/below a given threshold as quickly as possible. We present a finitehorizon search procedure to perform LSE in one dimension while optimally balancing both the final estimation error and the distance traveled during active learning for a fixed number of samples. A tuning parameter is used to trade off between the estimation accuracy and distance traveled. We show that the resulting optimization problem can be solved in closed form and that the resulting policy …


Techniques For Modeling Ocean Soundscapes: Detailed Description For Wind Contributionsa, Martin Siderius, Michael A. Ainslie, John Gebbie, Alexandra Schäfke, N Ross Chapman, Bruce Martin, Kay L. Gemba Nov 2024

Techniques For Modeling Ocean Soundscapes: Detailed Description For Wind Contributionsa, Martin Siderius, Michael A. Ainslie, John Gebbie, Alexandra Schäfke, N Ross Chapman, Bruce Martin, Kay L. Gemba

Electrical and Computer Engineering Faculty Publications and Presentations

Wind over the ocean creates breaking waves that generate air-filled bubbles, which radiate underwater sound. This wind-generated sound is a significant component of the ocean soundscape, and models are essential for understanding and predicting its impact. Models for predicting sound pressure level (SPL) from wind have been studied for many years. However, the terminology and definitions behind modeling approaches have not been unified, and ambiguity has led to differences in predicted SPL. The 2022 Ambient Sound Modeling Workshop was organized to compare ambient sound modeling approaches from different researchers. The main goal of the workshop was to quantify differences in …


Investigating Students' Expectations And Engagement In General And Organic Chemistry Laboratory Courses, Elizabeth B. Vaughan, Saraswathi Tummuru, Jack Barbera Oct 2024

Investigating Students' Expectations And Engagement In General And Organic Chemistry Laboratory Courses, Elizabeth B. Vaughan, Saraswathi Tummuru, Jack Barbera

Chemistry Faculty Publications and Presentations

Students’ expectations for their laboratory coursework are theorized to have an impact on their learning experiences and behaviors, such as engagement. Before students’ expectations and engagement can be explored in different types of undergraduate chemistry laboratory courses, appropriate measures of these constructs must be identified, and evidence of validity and reliability for the data collected with these instruments must be investigated. This study collected evidence related to response process validity, internal structure validity, and single administration reliability for version 2 of the Meaningful Learning in the Laboratory Instrument (MLLIv2) and a measure of student engagement in the undergraduate chemistry laboratory. …


Properties Of Generalized Polyhedral Convex Multifunctions, Ngoc Luan Nguyen, Mau Nam Nguyen, Dong Yen Nguyen Oct 2024

Properties Of Generalized Polyhedral Convex Multifunctions, Ngoc Luan Nguyen, Mau Nam Nguyen, Dong Yen Nguyen

Mathematics and Statistics Faculty Publications and Presentations

This paper presents a study of generalized polyhedral convexity under basic operations on multifunctions. We address the preservation of generalized polyhedral convexity under sums and compositions of multifunctions, the domains and ranges of generalized polyhedral convex multifunctions, and the direct and inverse images of sets under such mappings. Then we explore the class of optimal value functions defined by a generalized polyhedral convex objective function and a generalized polyhedral convex constrained mapping. The new results provide a framework for representing the relative interior of the graph of a generalized polyhedral convex multifunction in terms of the relative interiors of its …


Altitude-Driven Variations In Chrysophycean Stomatocyst Assemblages: Implications For Climate Reconstructions In The Three Parallel Rivers Of Yunnan Protected Area, China, Yanling Li, Qi Liu, Yangdong Pan, Wanting Pang Oct 2024

Altitude-Driven Variations In Chrysophycean Stomatocyst Assemblages: Implications For Climate Reconstructions In The Three Parallel Rivers Of Yunnan Protected Area, China, Yanling Li, Qi Liu, Yangdong Pan, Wanting Pang

Environmental Science and Management Faculty Publications and Presentations

The Three Parallel Rivers of Yunnan Protected Area (TPRYPA) is in the core area of the Hengduan Mountains, characterized by paralleling alternately high mountains and canyons that led to significant vertical temperature variation. Developing a climate transfer function for this region is crucial for both biodiversity protection and enhancing our understanding of feedback mechanisms between low-latitude and high-altitude areas in the context of global climate change. We investigated the chrysophycean stomatocyst assemblages from surface sediments of 46 high mountain lakes (altitude: 3244 to 5043 m) in the TPRYPA to assess the suitability of cysts in prediction of climate variability in …


Readiness Of Cybersecurity In The Usa Energy Industry, Aaron Cavanaugh Oct 2024

Readiness Of Cybersecurity In The Usa Energy Industry, Aaron Cavanaugh

Dissertations and Theses

Cybersecurity Readiness shows an organizations ability of applicant and application to be able to fully utilize computing resources through behaviors (e.g., training employees), practices, and processes, while managing risk through efficient controls in order to prevent, detect, and respond to outage scenarios using audit and assessment techniques. An evaluation of cybersecurity readiness for the USA energy industry assists industry decision makers to comprehensively assess readiness gaps for prioritizing a risk-based cybersecurity implementation plan. There is a currently a lack of a Multi-Criteria Decision Model (MCDM) to assist decision makers to comprehensively assess Readiness of Cybersecurity in the USA Energy Industry. …


Effects Of Spontaneous Curvature On Interfacial Adsorption And Collapse Of Phospholipid Monolayers, Bret A. Brandner, Shankar B. Rananavare, Stephen B. Hall Oct 2024

Effects Of Spontaneous Curvature On Interfacial Adsorption And Collapse Of Phospholipid Monolayers, Bret A. Brandner, Shankar B. Rananavare, Stephen B. Hall

Chemistry Faculty Publications and Presentations

To function effectively, pulmonary surfactant must adsorb rapidly to the alveolar air/water interface but avoid collapse from the surface when compressed to high interfacial densities. Prior studies show that phospholipids in the cylindrical monolayers of the inverse hexagonal (HII) phase adsorb quickly. The monolayers have negative curvature, defined by the concave shape of the hydrophilic face. Formation of the HII structures, however, involves significant disruption of chain-packing. Samples with significant spontaneous curvature, formed in the absence of applied force, may nonetheless have lamellar structures that optimize chain-packing. The experiments here tested whether planar lamellar bilayers formed by phospholipids with negative …


Graph Regularized Sparse L2,1 Semi-Nonnegative Matrix Factorization For Data Reduction, Anthony Rhodes, Bin Jiang, Jenny Jiang Oct 2024

Graph Regularized Sparse L2,1 Semi-Nonnegative Matrix Factorization For Data Reduction, Anthony Rhodes, Bin Jiang, Jenny Jiang

Mathematics and Statistics Faculty Publications and Presentations

Non-negative Matrix Factorization (NMF) is an effective algorithm for multivariate data analysis, including applications to feature selection, pattern recognition, and computer vision. Its variant, Semi-Nonnegative Matrix Factorization (SNF), extends the ability of NMF to render parts-based data representations to include mixed-sign data. Graph Regularized SNF builds upon this paradigm by adding a graph regularization term to preserve the local geometrical structure of the data space. Despite their successes, SNF-related algorithms to date still suffer from instability caused by the Frobenius norm due to the effects of outliers and noise. In this paper, we present a new L2,1 SNF algorithm that …


Cross-Track Seabed Imaging And Buried Object Detection With A Multibeam Sonar, Charles W. Holland, Samuel Pinson, Daniel L. Orange, Cody R. Henderson Oct 2024

Cross-Track Seabed Imaging And Buried Object Detection With A Multibeam Sonar, Charles W. Holland, Samuel Pinson, Daniel L. Orange, Cody R. Henderson

Electrical and Computer Engineering Faculty Publications and Presentations

What lies underneath the ocean floor is of interest to a wide variety of disciplines. The focus here is imaging the upper tens of meters of material beneath the seafloor. The sub-bottom profiler is a valuable tool to that end, producing a 2-D image in depth below the seafloor and along the track of the ship. Geoscientists and engineers are frequently interested in not only the subseabed beneath the ship but also either side or cross-track of the ship. We show an approach to cross-track imaging using a low-frequency multibeam sub-bottom profiler. The main result is the detection of a …


Causal Effect Estimation In Survival Analysis With High Dimensional Confounders, Fei Jiang, Ge Zhao, Rosa Rodriguez-Monguio, Yanyuan Ma Oct 2024

Causal Effect Estimation In Survival Analysis With High Dimensional Confounders, Fei Jiang, Ge Zhao, Rosa Rodriguez-Monguio, Yanyuan Ma

Mathematics and Statistics Faculty Publications and Presentations

With the ever advancing of modern technologies, it has become increasingly common that the number of collected confounders exceeds the number of subjects in a data set. However, matching based methods for estimating causal treatment effect in their original forms are not capable of handling high-dimensional confounders, and their various modified versions lack statistical support and valid inference tools. In this article, we propose a new approach for estimating causal treatment effect, defined as the difference of the restricted mean survival time (RMST) under different treatments in high-dimensional setting for survival data. We combine the factor model and the sufficient …


A Concept Of Controlling Grover Diffusion Operator: A New Approach To Solve Arbitrary Boolean-Based Problems, Ali Al-Bayaty, Marek A. Perkowski Oct 2024

A Concept Of Controlling Grover Diffusion Operator: A New Approach To Solve Arbitrary Boolean-Based Problems, Ali Al-Bayaty, Marek A. Perkowski

Electrical and Computer Engineering Faculty Publications and Presentations

A controlled-diffusion operator for Boolean oracles is designed as a new approach for Grover’s algorithm to search for solutions for arbitrary logical structures of such oracles, since the Grover diffusion operator is not able to find correct solutions for some logical structures of Boolean oracles. We also show that the Phase oracles do not work sometimes correctly using the Grover diffusion operator. Our proposed controlled-diffusion operator relies on the states of output qubit, as the reflection of Boolean decisions from a Boolean oracle without relying on the phase kickback. We prove that on many examples of Boolean and Phase oracles …


The Carbon Crater: Comparing Anthropogenic Greenhouse Gas Emissions To Historical Planetary Events, Hal T. Nelson, Paul Reynolds, Brian W. Jewett Oct 2024

The Carbon Crater: Comparing Anthropogenic Greenhouse Gas Emissions To Historical Planetary Events, Hal T. Nelson, Paul Reynolds, Brian W. Jewett

Public Administration Faculty Publications and Presentations

Equilibrium climate sensitivity modeling relies heavily on paleoclimate records that were affected by meteorite impacts and volcanic explosions. This paper conducts a thought experiment by re-assembling known data and theories to shed new light on anthropogenic carbon waste. Anthropogenic activity, meteorite impacts and volcanic explosions all extract material from the Earth’s crust and deposit it in the atmosphere. This thought experiment tests if the mass of anthropogenic greenhouse gas emissions from 1851 to 2021 is comparable to the mass of atmospheric emissions from historical planetary events. Approximately 3.60 trillion tons of anthropogenic carbon dioxide equivalents are converted into volume and …


Re-Evaluating Hypertragulid Diversity In The John Day Basin, Oregon, Usa, Nicholas A. Famoso, Lana K. Jewell Oct 2024

Re-Evaluating Hypertragulid Diversity In The John Day Basin, Oregon, Usa, Nicholas A. Famoso, Lana K. Jewell

Geology Faculty Publications and Presentations

Despite their relative abundance, members of the family Hypertragulidae (Artiodactyla, Mammalia) have proved a conundrum regarding species diversity in the Turtle Cove Member (Oligocene) of the John Day Formation, located in central and eastern Oregon. Three species and two separate genera are described in the area, but previous research lacks statistical support for this level of variation. We use coefficients of variation (V) on measurements of dentition and astragali of hypertragulid specimens designated Hypertragulus hesperius, Hypertragulus minutus, and Nanotragulus planiceps as a metric for determining whether there were multiple species present in the population. Asymptotic and modified signed-likelihood ratio V …


Oregon State Rank Assessment For Sheldon Tui Chub (Siphateles Bicolor Eurysoma), Eleanor P. Gaines Oct 2024

Oregon State Rank Assessment For Sheldon Tui Chub (Siphateles Bicolor Eurysoma), Eleanor P. Gaines

Institute for Natural Resources Publications

Oregon state conservation status assessment for Sheldon tui chub (Siphateles bicolor eurysoma) using NatureServe methodology, 2024.


Stability Analysis For Acoustic Waveguides. Part 3: Impedance Boundary Conditions, Leszek Demkowicz, Jay Gopalakrishnan, Norbert Heuer Oct 2024

Stability Analysis For Acoustic Waveguides. Part 3: Impedance Boundary Conditions, Leszek Demkowicz, Jay Gopalakrishnan, Norbert Heuer

Mathematics and Statistics Faculty Publications and Presentations

A model two-dimensional acoustic waveguide with lateral impedance boundary conditions (and outgoing boundary conditions at the waveguide outlet) is considered. The governing operator is proved to be bounded below with a stability constant inversely proportional to the length of the waveguide. The presence of impedance boundary conditions leads to a non self-adjoint operator which considerably complicates the analysis. The goal of this paper is to elucidate these complications and tools that are applicable, as simply as possible. This work is a continuation of prior waveguide studies (where self-adjoint operators arose) by J. M. Melenk et al. (2023), and L. Demkowicz …


Exploring Teacher Perspectives Of Stem Outreach Sessions, Jennifer M. Jakobi, Rebecca Mccullough, Sabre Cherkowski, Haizley Trevor-Smith Oct 2024

Exploring Teacher Perspectives Of Stem Outreach Sessions, Jennifer M. Jakobi, Rebecca Mccullough, Sabre Cherkowski, Haizley Trevor-Smith

Northwest Journal of Teacher Education

Teachers have a responsibility to create and foster engaging learning environments which encourage underrepresented persons in Science, Technology, Engineering, and Mathematics (STEM). Outreach programs have been shown to increase STEM engagement of students. We use a positive psychology lens to investigate STEM outreach and teacher wellbeing. This exploratory study uses a survey and focus group to assess how a STEM outreach program can create teacher feelings of support, confidence, and enjoyment. Results demonstrate that most teachers felt more confident in teaching STEM following the STEM-mentor facilitated outreach sessions. The positive benefits to teacher wellbeing from outreach program mentorship, is discussed.


Projected Loss Of Rock Glacier Habitat In The Contiguous Western United States With Warming, Abigail C. Lute, John T. Abatzoglou, Andrew G. Fountain, Timothy C. Bartholomaus Oct 2024

Projected Loss Of Rock Glacier Habitat In The Contiguous Western United States With Warming, Abigail C. Lute, John T. Abatzoglou, Andrew G. Fountain, Timothy C. Bartholomaus

Geology Faculty Publications and Presentations

Rock glaciers support alpine biodiversity and may respond more slowly to warming than snow or glaciers. While responses of snow and glaciers to climate change are relatively well understood, a robust assessment of rock glacier environmental niche, future distributions of rock glaciers and potential for development of rock glaciers from current glaciers is lacking. Using process-relevant, high-resolution environmental descriptors, we develop a species distribution model of the topographic, geologic and hydroclimatic niche of rock glaciers that provides novel estimates of potential rock glacier distributions for different climates. We identify mean annual air temperature and headwall area as the dominant controls …


Oregon State Rank Assessment For Goose Lake Tui Chub (Siphateles Bicolor Thalassinus), Jesse Laney Oct 2024

Oregon State Rank Assessment For Goose Lake Tui Chub (Siphateles Bicolor Thalassinus), Jesse Laney

Institute for Natural Resources Publications

Oregon state conservation status assessment for Goose Lake tui chub (Siphateles bicolor thalassinus) using NatureServe methodology, 2024.


Tabular Data-Centric Ai: Challenges, Techniques And Future Perspectives, Yanjie Fu, Dongjie Wang, Hui Xiong, Kunpeng Liu Oct 2024

Tabular Data-Centric Ai: Challenges, Techniques And Future Perspectives, Yanjie Fu, Dongjie Wang, Hui Xiong, Kunpeng Liu

Computer Science Faculty Publications and Presentations

Tabular data are the most widely used data formats in almost every application domain, such as, biology, ecology, and material science. The purpose of tabular data-centric AI is to use AI to augment the predictive power of tabular data to get better AI. Tabular data-centric AI is essential because it can reconstruct distance measures, reshape discriminative patterns, and improve data AI readiness (structural, predictive, interaction, and expression levels), which is significant in industries and real-world deployments. Therefore, our tutorial is designed to capture the interest of professionals with expertise in artificial intelligence, machine learning, and data mining, as well as …


On Localization Of Eigenfunctions Of The Magnetic Laplacian, Jeffrey S. Ovall, Hadrian Quan, Robyn Reid, Stefan Steinerberger Oct 2024

On Localization Of Eigenfunctions Of The Magnetic Laplacian, Jeffrey S. Ovall, Hadrian Quan, Robyn Reid, Stefan Steinerberger

Mathematics and Statistics Faculty Publications and Presentations

Let Ω ⊂ ℝd and consider the magnetic Laplace operator given by H(A) = (–i∇ – A(x))2, where A : Ω → ℝd, subject to Dirichlet boundary conditions. For certain vector fields A, this operator can have eigenfunctions, H(A)ψ = λψ, that are highly localized in a small region of Ω. The main goal of this paper is to show that if |ψ| assumes its maximum at x0 ∈ Ω, then A behaves 'almost' like a conservative vector field in a -neighborhood of x0 in a precise sense. In particular, we expect localization in regions where |curl A| is small. …


Bht-Qaoa: The Generalization Of Quantum Approximate Optimization Algorithm To Solve Arbitrary Boolean Problems As Hamiltonians, Ali Al-Bayaty, Marek Perkowski Oct 2024

Bht-Qaoa: The Generalization Of Quantum Approximate Optimization Algorithm To Solve Arbitrary Boolean Problems As Hamiltonians, Ali Al-Bayaty, Marek Perkowski

Electrical and Computer Engineering Faculty Publications and Presentations

A new methodology is introduced to solve classical Boolean problems as Hamiltonians, using the quantum approximate optimization algorithm (QAOA). This methodology is termed the “Boolean-Hamiltonians Transform for QAOA” (BHT-QAOA). Because a great deal of research and studies are mainly focused on solving combinatorial optimization problems using QAOA, the BHTQAOA adds an additional capability to QAOA to find all optimized approximated solutions for Boolean problems, by transforming such problems from Boolean oracles (in different structures) into Phase oracles, and then into the Hamiltonians of QAOA. From such a transformation, we noticed that the total utilized numbers of qubits and quantum gates …


A Coupled Spatial-Network Model: A Mathematical Framework For Applications In Epidemiology, Hannah Kravitz, Christina Duron, Moysey Brio Oct 2024

A Coupled Spatial-Network Model: A Mathematical Framework For Applications In Epidemiology, Hannah Kravitz, Christina Duron, Moysey Brio

Mathematics and Statistics Faculty Publications and Presentations

There is extensive evidence that network structure (e.g., air transport, rivers, or roads) may significantly enhance the spread of epidemics into the surrounding geographical area. A new compartmental modeling framework is proposed which couples well-mixed (ODE in time) population centers at the vertices, 1D travel routes on the graph’s edges, and a 2D continuum containing the rest of the population to simulate how an infection spreads through a population. The edge equations are coupled to the vertex ODEs through junction conditions, while the domain equations are coupled to the edges through boundary conditions. A numerical method based on spatial finite …


Pathos, Fall 2024, Portland State University. Student Publications Board Oct 2024

Pathos, Fall 2024, Portland State University. Student Publications Board

Pathos

Editor: Adriana Stanzione


The Hydraulically Smooth Limit Of Flow Over Surfaces With Spanwise Heterogeneity, Haosen Xu, George Ilhwan Park, Xiang Yang, Xiaowei Zhu Oct 2024

The Hydraulically Smooth Limit Of Flow Over Surfaces With Spanwise Heterogeneity, Haosen Xu, George Ilhwan Park, Xiang Yang, Xiaowei Zhu

Mechanical and Materials Engineering Faculty Publications and Presentations

Wall slip is conventionally obtained through riblets or grooves. As riblets are macroscopic objects, it is usually not practical to discuss slip patterns at the hydraulically smooth limit. Per Nikuradse, the smooth limit is when the characteristic length of the surface pattern is comparable to the viscous length scale. Recent studies show the possibility of slip at the microscopic scale, making slip patterns at the hydraulically smooth limit relevant. In this study, we leverage a high-fidelity pseudo-spectral code and study flow over surfaces featuring alternating strips of slip and no-slip wall conditions. The wavelength of the surface pattern, denoted as …


Information-Theoretic Modeling Of Categorical Spatiotemporal Gis Data, David Percy, Martin Zwick Sep 2024

Information-Theoretic Modeling Of Categorical Spatiotemporal Gis Data, David Percy, Martin Zwick

Geology Faculty Publications and Presentations

An information-theoretic data mining method is employed to analyze categorical spatiotemporal Geographic Information System land use data. Reconstructability Analysis (RA) is a maximum-entropy-based data modeling methodology that works exclusively with discrete data such as those in the National Land Cover Database (NLCD). The NLCD is organized into a spatial (raster) grid and data are available in a consistent format for every five years from 2001 to 2021. An NLCD tool reports how much change occurred for each category of land use; for the study area examined, the most dynamic class is Evergreen Forest (EFO), so the presence or absence of …


Exploring The Relationship Between Covid-19 Transmission And Population Mobility Over Time, Tanmoy Bhowmik, Naveen Eluru Sep 2024

Exploring The Relationship Between Covid-19 Transmission And Population Mobility Over Time, Tanmoy Bhowmik, Naveen Eluru

Civil and Environmental Engineering Faculty Publications and Presentations

This study explores the dynamic relationship between COVID-19 transmission and transportation mobility, with an emphasis on understanding the time-varying bidirectional interplay across the different phases of the pandemic. To gain insight into this relationship, we analyzed county-level data on transmission and mobility patterns from the United States over a 74-week period using a comprehensive list of factors including: temporal factors, socio-demographics, health indicators, health care infrastructure attributes, and spatial factors. For our analysis, we proposed a simultaneous econometric model system that explicitly accounts for the bidirectional relationship between COVID-19 transmission and mobility patterns while also accounting for the influence of …


Minimal Separating Sets In Surfaces, Christopher Nelson Aagaard Sep 2024

Minimal Separating Sets In Surfaces, Christopher Nelson Aagaard

Dissertations and Theses

Given a connected topolgical space X, we say that L ⊆ X is a minimal separating set if removing L from X gives a disconnected surface, butremoving any proper subset of L leaves the surface connected. We classify which embeddings of topological graphs are minimal separating in an orientable surface X with genus g, and construct a computer program to compute the number of such embeddings, and the number of topological graphs which admit such an embedding for g ≤ 5.