Mathematics Commons^™

Collaborative Research: Cif: Medium: Foundations Of Robust Deep Learning Via Data Geometry And Dyadic Structure, Kevin Moon

Funded Research Records

No abstract provided.

Representation Theory In Unoriented And Non-Semisimple Physics, Matthew Bruce Young

Funded Research Records

No abstract provided.

Understanding Enso Through Mathematical Models, Maria I. Sanchez Muniz

Open Educational Resources

This assignment introduces students to conceptual models of the El Niño–Southern Oscillation (ENSO) and guides them through a structured investigation of their physical and mathematical foundations. Students analyze the recharge–oscillator and delayed–oscillator frameworks, explore how differential equations capture ocean–atmosphere interactions, and evaluate parameter-driven changes in oscillatory behavior. A key component of the work is the guided use of generative AI as a research tool: students employ AI models to locate peer-reviewed literature, interrogate model extensions, and refine their understanding of complex mechanisms, while synthesizing all final explanations in their own words. By blending classical climate modeling with modern AI-supported inquiry, …

Systematics And Systems Theory: Reconstructability Analysis Of The Tetrad, Martin Zwick

Complex Systems Faculty Publications and Presentations

This talk discusses the relationship between systems theory, specifically Reconstructability Analysis, and Systematics, a systems theory-like framework of number symbolism developed by John G. Bennett, which he presented in his four-volume magnum opus, The Dramatic Universe. The talk, given to a community of people interested in Bennett's ideas, focuses on Martin Zwick's paper "Ideas and Graphs: the Tetrad of Activity" archived at https://archives.pdx.edu/ds/psu/36249.

A (Mini) Mathematics Research Experience In A Math Teachers’ Circle Session, Michelle Manes, Linda Venenciano, Seanyelle Yagi

Journal of Math Circles

We describe a single Math Teachers’ Circle session during which a group of teachers collectively engaged in a “mini mathematics research experience.” This provides a model for providing research experiences for mathematics teachers through content-based professional development programs. We conjecture that these experiences will have many of the same benefits as research experiences for teachers in lab sciences.

Timss 2023 – Infographic: Future Pd Needs Of Maths Teachers, Jo Earp

Teacher infographics

The IEA’s Trends in International Mathematics and Science Study (TIMSS) is a global assessment measuring student achievement in years 4 and 8. Teachers from participating schools also complete a questionnaire. Today’s infographic looks at the topics that mathematics teachers reported needing professional development on in the future.

(R2127) On 2-Absorbing Hesitant Primary Fuzzy Ideals Of Rings, B. Anitha, M. Vidhya

Applications and Applied Mathematics: An International Journal (AAM)

By presenting 2-absorbing hesitant primary fuzzy ideals, we begin the investigation of a generalisation of hesitant primary fuzzy ideals (HPRFI) in rings in this research. The concepts of a weakly completely 2-absorbing hesitant primary fuzzy ideal (WC2-AHPRFI) and a Weakly completely 2-absorbing hesitant fuzzy ideal (WC2-AHFI) are developed, and their structural features and attributes are examined. We introduce the idea of a 2-absorbing hesitant K-fuzzy ideal (2-AHK-FI), 2-absorbing hesitant K-primary fuzzy ideal (2-AHK-PRFI) and examine a few of its characteristics.

(R2122) Analysis Of Halo Orbits In The Elliptical R3bp With Mass Variation, Majhar Ali, Abdullah .

Applications and Applied Mathematics: An International Journal (AAM)

The elliptic restricted three-body problem investigates the motion behaviour of the variable mass infinitesimal body under the gravitational forces of the radiated oblate primary and dipole secondary. The equations of motion of the infinitesimal body are determined using Jeans law and Meshcherskii space time transformations. Using the Lindstedt-Poincaré method, we perform the solutions of the equations of motion. With the use of these solutions and the equations of motion, we numerically illustrate the time series, phase spaces, projections and the Halo orbits.

(R2094) On Mds Bisymmetric Rhotrices Using Self-Dual Bases And Conjugate Elements Of Finite Fields, Shalini Gupta, Ruchi Narang, Manpreet Singh

Applications and Applied Mathematics: An International Journal (AAM)

Bisymmetric matrices have wide range of applications in statistics, engineering problems, information theory and computer science including coding theory and cryptography. In cryptography, a rhotrix being a couple matrix doubles the security of the cryptosystem. Here, we construct maximum distance separable (MDS) bisymmetric rhotrices using self-dual bases and conjugate elements of finite fields. MDS rhotrices are very crucial for the designing of block ciphers and hash functions in cryptography.

Error Reduction Methodology And Data Simulation For Interval Data, Ranik Christopher Jelinek

Undergraduate Honors Capstone Projects

Chronic kidney disease (CKD) is a progressive condition affecting hundreds of millions of individuals worldwide. However, clinical datasets often record continuous laboratory measurements as categorical intervals rather than precise numerical values. This interval-censored structure presents methodological challenges for standard regression-based classifiers. This study compares three strategies for handling interval-valued predictors prior to fitting a logistic LASSO model: (1) midpoint imputation, which replaces each interval with its arithmetic center; (2) ordinal encoding, which maps intervals to integer ranks; and (3) a Monte Carlo simulation approach, which repeatedly samples uniformly from each observed interval and averages predictions across replications. Using a 10-fold …

A Persistent Homology Framework For Scrna-Seq: Assessing Clustering Robustness And Quantifying Preprocessing And Integration Effects On Topological Features., Jonah Daneshmand

Electronic Theses and Dissertations

As single-cell RNA sequencing (scRNA-seq) data expands, robust methods for integrating diverse datasets are critical. This dissertation applies Persistent Homology (PH), a technique from Topological Data Analysis (TDA), to a collection of scRNA-seq datasets spanning eight tissue types to quantify how data integration affects topological features and biological interpretability. We assessed global topological structure using Betti curves, Euler characteristics, and persistence landscapes across raw, normalized, and integrated data representations. Our analysis revealed a performance inversion: while conventional methods excelled on unintegrated data, high-granularity topological methods, particularly those sensitive to global data structure, became superior after integration. This suggests a synergy …

Fast Computation Of The Friction Stir Welding Process With Model Order Reduction, Joshua Kay

All Graduate Theses and Dissertations, Fall 2023 to Present

Friction stir welding (FSW) is a manufacturing process used to join materials through intense heat and pressure. To better understand and optimize this FSW process, mathematical models incorporating non-Newtonian Navier-stokes equations for large plastic deformation and heat equation for the heat transfer are used to simulate the FSW process. However, solving these coupled and nonlinear equations with high accuracy requires significant computational power and time. This thesis has applied model order reduction, more precisely the Proper Orthogonal Decomposition (POD) and Discrete Empirical Interpolation Method (DEIM), to efficiently solve the FSW system in low-dimensional space. Slight modifications are made regarding the …

The Impact Of Transmission Thresholds Across Multiple Scales On The Spread Of Chronic Wasting Disease In Wisconsin, Jen Mcclure

All Graduate Theses and Dissertations, Fall 2023 to Present

Wildlife diseases can be difficult to control once they are established. This is especially true when they spread through contact with infectious material left in the environment. One such disease is chronic wasting disease (CWD), a fatal illness affecting deer and related species in North America and other regions. CWD is caused by prions, misfolded proteins that can remain infectious for years after shedding by infected hosts.

Recent research shows that CWD infection does not always follow from the gradual accumulation of prions through small contact events. Rather, an individual may need to encounter a certain prion dose all at …

Wacsaw: An Adaptive, Statistical Method To Classify Movement Into Sleep And Wakefulness States, Austin Vandegriffe, V. A. Samaranayake, Matthew S. Thimgan

Mathematics and Statistics Faculty Research & Creative Works

Wearable actimeters can improve our understanding of sleep in the natural environments. Current algorithms may produce inaccuracies in specific individuals and circumstances, such as quiet wakefulness. New hardware allows data collection at higher frequencies enabling sophisticated analytical methods. We have developed a novel statistical algorithm, the Wasserstein Algorithm for Classifying Sleep and Wakefulness (WACSAW), to identify behavioral states from recordings of everyday movement. WACSAW employs optimal transport techniques to identify segments with differing activity variability. Functions characterizing the segments' movement distributions were clustered into two groups using a k-nearest neighbors and labeled as sleep or wake based on their proximity …

(R2137) Smarandache Curved Ruled Surfaces And Their Characterizations According To Modified Orthogonal Frame In E^3, Gülnur Şaffak Atalay

Applications and Applied Mathematics: An International Journal (AAM)

In this study, the ruled surfaces generated by Smarandache curves are expressed according to the modified orthogonal frame defined according to both curvature and torsion of the given unit speed curve in 3-dimensional Euclidean space; some special characterizations of these surfaces such as developability, striction curves, distribution parameters are given. In addition, some examples of these surfaces are given in graphical form. We use Maple to draw the graphs of the examples.

Investigating The Efficiency Of Ingan P-N-P-N Homojunction Solar Cells, Moath Alhejji, Mohammad Alavijeh, Jacob Kupernik, Mirsaeid Sarollahi, Abbas Jammali, Seyed Taghavi, Reem Alhelais, Md Hel Uddin Maruf, Morgan Ware

Electrical Engineering and Computer Science Faculty Publications and Presentations

This research investigates the development of a novel p-n-p-n homostructure solar cell, through semiconductor simulations using the Nextnano software. InGaN was used as a model system in order to achieve a bandgap with optimized efficiency for a p-n homojunction solar cell. By increasing the uniform doping concentration from 1.5*10(16) cm(-3) to 1.5*10(17) cm(-3), the open circuit voltage (V-oc) increased while the short-circuit current density (J(sc)) decreased, as expected in simple p-n junctions. The p-n-p-n structure achieved a peak efficiency of 32.91% at a doping level of 6.5*10(16) cm(-3), a similar to 7% improvement over a conventional p-n junction's 25.31% efficiency …

Array Of Mini-Graphene-Silicon Solar Cells Intermittently Recharges Storage Capacitors Powering A Temperature Sensor, Ashaduzzaman, Syed M. Rahman, Md R. Kabir, James M. Mangum, Hung Do, Gordon Carichner, David Blaauw, Paul M. Thibado

Physics Faculty Publications and Presentations

Developing autonomous sensor systems that draw power from the ambient environment is a critical step for creating the Internet of Things. In this study, the authors built dozens of graphene-based solar cells, wire bonded them into standard packages, and characterized the current-voltage characteristics of each under illumination. Next, solar cells were connected in series to increase the output voltage. Three different sets of solar cells were used to charge three storage capacitors to the voltage levels required by our temperature sensor. The storage capacitors require only a few minutes to charge, yet power the sensor system for more than 24 …

Implications Of The Attenuated Allee Effect On Population Dynamics, Dana Strong

All Graduate Theses and Dissertations, Fall 2023 to Present

The Allee effect is an ecological phenomenon characterized by a per capita growth rate that increases as the population size increases in the context of low population density. The Allee effect can lead to rapid extinction events. Consequently, ecologists can attempt to control the strength of the Allee effect to help increase the population (in the case of endangered species) or decrease the population (in the case of parasites or pests).

This research aimed to study not the strength of the Allee effect, but the intensity of the Allee effect, or how rapidly cooperation between individuals causes the per capita …

Content And Consequences: Impact Of Representation In Stem Higher Education Instructional Content On Marginalized Students, Nichole Ventura

Doctorate in Education

This qualitative study examined representation of historically marginalized students in STEM instructional content at the higher education level and its impact on their learning experiences. Despite growing diversity initiatives in STEM enrollment, curricular materials often fail to reflect the identities of underrepresented students. Using critical theory and interpretivist approaches, this research investigated how representation—or its absence—shapes students' sense of belonging, academic identity formation, and persistence. Through semi-structured interviews with undergraduate students from historically marginalized backgrounds, and purposeful sampling, this study captured the lived experiences of students engaging with STEM instructional materials. Interview protocols explored how students perceive their representation in …

Self-Assessment In Calculus I, Bertha Naa Dei Neequaye

All Graduate Theses and Dissertations, Fall 2023 to Present

The purpose of this research investigate how undergraduate students in Calculus I at Utah State University learn and reflect on their level of understanding of Calculus I. In the study, self-assessment practices refer to students reflecting on what they have learned, rating their level of understanding and providing examples that illustrate their level of understanding. The structured and unstructured self-assessment rubrics were the two types of self-assessment rubrics used in the study. The structured self-assessment rubric provides a clear list of objectives of Calculus I topics for students to rate themselves on, while the unstructured self-assessment rubric is an open …

Machine Learning Applications: Cell Tracking And Nonparametric Estimation Of Non-Smooth Divergences, Mina Mahbub Hossain

All Graduate Theses and Dissertations, Fall 2023 to Present

This thesis brings together two important research directions: how to compare different sets of data more accurately, and how to better understand how brain cancer cells move and change shape.

In the first part, we look at a problem in statistics: measuring how different two data sources are from each other. Traditional methods often make strong assumptions, which may not always hold in real situations. Our approach avoids those assumptions by using an ensemble method, a way of combining many weak estimators into one stronger result. This makes the method more flexible and reliable, especially when dealing with complex or …

Combinatorics Of Trees Via Derivatives Of Polynomial Functors In Homotopy Type Theory, Warren David Hatton

Boise State University Theses and Dissertations

Polynomial functors are, essentially, polynomials whose variables take values in sets, groupoids, or some other suitable category, rather than in numbers. In this thesis, we will explore three related aspects of polynomial functors over $\infty$-groupoids in the framework of homotopy type theory: first, polynomial functors provide a foundation for inductively defined data types as wellfounded trees; second, polynomial functors have a notion of derivative which, viewed in light of the connection to data types, yields a computational interpretation of differentiation; and third, suitably finite polynomial functors over (higher) groupoids yield categorified generating functions, and thus subsume the theory of combinatorial …

A Comparative Study Of Novel Methods For Variances, Taoreed Muritala

Boise State University Theses and Dissertations

Understanding variability is fundamental to knowledge advancement across various disciplines, including manufacturing, clinical research, biology and genetics. Population variances play a crucial role in processes such as quality control, treatment evaluation and the interpretation of biological mechanisms. However, statistical procedures for comparing variances across multiple populations remain less developed than those for comparing means. Classical omnibus tests, such as Bartlett's and Levene's, can detect overall variance heterogeneity but fail to identify which populations differ, thereby limiting their usefulness in multi-population analyses and increasing the risk of inflated family-wise error rates through repeated testing.

This thesis develops and evaluates three multiple …

Abelian Sandpile Models On Edge Periodic Graphs, Payton Lyons

Boise State University Theses and Dissertations

The abelian sandpile model is a Markov chain that is able to decompose any recurrent configuration into a basic alive divisor, some amount of sand placed on the sink vertex, and a series of vertex firings. In this paper we begin to explore some of the dynamics of this system when the edges of the graph are allowed to alternate between two different edge sets. This system will be framed in a similar fashion as the classical model, and then some basic numerical simulations were used to observe the threshold behavior of the system. We lay some of the initial …

Scaling Wind Farm Layout Optimisation To Meet Uk Energy Demands, Grace Richardson

The Plymouth Student Scientist

This research aims to explore the Wind Farm Layout Optimisation Problem (WFLOP) through both single- and multi-objective optimisation, to show that it can be used to create farm layouts that provide enough power for all homes in the UK. We highlight the intricacies of the problem, including the application of different algorithms and models, and the challenges of scaling the models to achieve optimal results. We employ both a Hill Climbing Algorithm (HCA) and an evolutionary algorithm (NSGA-II) to obtain wind farm layouts, and compare these to the well-known results proposed by Mosetti et al. Moreover, we present a novel …

Connections On Manifolds: A Modern Approach To Classical Differential Geometry, Jed Allen Wilshire

Theses and Dissertations

The purpose of this thesis is to connect modern differential geometry concepts to the classical differential geometry study of surfaces, specifically spheres. This thesis will cover the topics of Riemannian manifolds, tangent spaces, vectors, vector fields, the connection of Levi-Civita, the Christoffel symbols, and Riemannian curvature. Each concept will be demonstrated on the well known unit sphere manifold.

A Computational Approach To Ramanujan-Type Congruences For Products Of Level 13, Aiden Michael Lalonde

Theses and Dissertations

In this thesis, we find products that are modular forms of level 13 whose Fourier coefficients satisfy certain congruences. These products are constructed in terms of integer powers of Klein forms and the Dedekind eta function. The products that are modular forms for Γ1 (13) have vectors of exponents that are elements of a bounded polytope. A parameterization for this polytope allows us to find a complete set of products that are modular forms for Γ1 (13). The corresponding graded ring of modular forms containing these products is constructed from a finite set of generators. These generators satisfy a finite …

A Leslie System For A Demographic Simulation: From An Actuarial Point Of View, David Kings

Electronic Theses and Dissertations

This thesis develops a discrete stochastic linear systems interpretation of age–stage demographic evolution grounded in Leslie operators and realized in a discrete-event simulation implemented with salabim. The central claim is that one annual cycle of the simulation constitutes a cone-preserving, stochastic affine transformation on a high- dimensional population state vector indexed by age, sex, marital status, household type, employment, and education, and that the composition of yearly operators yields a random matrix product whose top Lyapunov exponent is the stochastic counterpart of the Perron–Frobenius growth rate (Caswell, 2001; Tuljapurkar, 1997)[1, 2]. The actuarial bridge is constructed by mapping simulated survival …

Robustness Of Network Inference Algorithms Under Network Class Misspecification, Roberto Ceja

Electronic Theses, Projects, and Dissertations

Inferring phylogenies in the presence of hybridization remains a difficult problem. As a result, many current methods for reconstructing phylogenetic networks are restricted to a simple class of networks known as level-1. This restriction arises from theoretical considerations rather than empirical evidence, with real data possibly arising from complex networks. In this work, we evaluate the robustness of two level-1 network inference methods, SNaQ and NANUQ+, through a simulation study, when the input data originates from a more complex network. Specifically, we investigate whether these methods can accurately recover important features of the true species network, such as the circular …

Predictors Of Math Identity In U.S. High School Students, Edwin Flores

Electronic Theses, Projects, and Dissertations

This study explored factors related to high school students’ sense of math identity. Data from the High School Longitudinal Study of 2009 was used which is a nationally representative dataset from the National Center of Education Statistics (NCES). The sample is representative of U.S. high schoolers who began ninth grade in 2009. Multiple regression analysis was performed and factors relating to students’ prior mathematics coursework and attitudes about mathematics were found to predict students’ mathematics identity.

Keywords. Mathematics, identity, high school students