Digital Commons Network^™

Student Worksheets Based On The Local Wisdom Of Besilek Serawai For Sixth-Grade Elementary Science Learning, Mice Agustin, Tomi Hidayat, Irwandi Irwandi

Jurnal Pendidikan Sains

This study aims to develop a Student Worksheet (Lembar Kerja Peserta Didik [LKPD]) based on the local wisdom of Besilek Serawai for sixth-grade elementary science education and to evaluate its validity. The study employed the ADDIE development model, consisting of five stages: Analyze, Design, Develop, Implement, and Evaluate. The developed LKPD integrates Besilek Serawai, a traditional martial art of the Seluma community, with the concept of the human locomotor system in science instruction. The worksheet was validated by two subject-matter experts and two media experts. Material validation yielded an average score of 4.26, equivalent to a validity percentage of 85.2%, …

You Mean What? Commognitive Conflict In Resolving Contextual Logarithm Problems, Endrayana Putut Laksminto Emanuel, Fatkul Anam, Radhitya Duta Pradana, Anik Kirana, Sikky El Walida

Jurnal Pendidikan Sains

Students’ approaches to solving contextual mathematics problems involving logarithms vary significantly due to differences in their prior mathematical understanding. These differences may trigger commognitive conflict during the interpretation and reasoning processes when students attempt to construct mathematical meaning from contextual situations. This qualitative study aimed to explore how commognitive conflict emerges as a mechanism of mathematical interpretation in students’ discourse while solving logarithmic contextual problems. Twenty students participated in the study and were grouped based on their performance. One student was selected as the main research subject for an in-depth analysis. The findings reveal that commognitive conflict appeared in two …

The Effect Of Project-Based Learning Model On Entrepreneurship (Pjbl-E) With A Deep Learning Approach On Students' Problem-Solving And Cognitive Skills, Ricce Oktasari, Irwandi Irwandi, Siti Darwa Suryani

Jurnal Pendidikan Sains

This study aims to examine the effect of the Entrepreneurship-based Project Based Learning (PjBL-E) model integrated with a pedagogical Deep Learning approach on students’ problem-solving skills and cognitive learning outcomes in biology learning. The novelty of this study lies in the integration of entrepreneurship values and pedagogical deep learning principles into Project Based Learning to create contextual and meaningful learning experiences. Entrepreneurship integration encourages students to develop innovative products, identify real-world problems, and apply biological concepts in practical and socio-economic contexts. Meanwhile, the pedagogical Deep Learning approach promotes reflective thinking, conceptual understanding, critical analysis, and the ability to connect theory …

Cardiovascular Disease Subtypes And Alzheimer's Disease: Phenotypic And Genetic Associations In The Uk Biobank And All Of Us Research Program, Aili Toyli, Chen Zhao, Kuan Jui Su, Hui Shen, Hong Wen Deng, Qing Hui Chen, Qiuying Sha, Weihua Zhou

Michigan Tech Publications

BACKGROUND: Cardiovascular disease (CVD) and Alzheimer's disease (AD) are major public health concerns that share overlapping risk factors and potential mechanistic pathways. Although vascular contributions to cognitive decline are well documented, the specific relationships between AD and different CVD subtypes remain poorly understood. METHODS: In this cross-sectional study, we examined associations between AD and 11 CVD subtypes using logistic regression models in 2 large biobanks: the UK Biobank (n=502 133) and the All of Us Research Program (n=287 011). Models were adjusted for demographic, lifestyle, and clinical covariates. We also explored genetic overlap between AD and CVD traits through proximity-based …

New Studies In Lattice-Based Cryptography, Quantum Algorithms, And Privacy-Preserving Computation, Hansraj Jangir

Electronic Theses and Dissertations

Classical public-key cryptographic schemes primarily rely on the presumed hardness of the integer factorization and discrete logarithm problems. However, Shor’s algorithm demonstrates that both problems can be solved efficiently on a sufficiently powerful quantum computer. This breakthrough motivated the search for quantum-resistant hard assumptions. The assumptions based on lattices are one of the primary candidates in post-quantum cryptography due to their strong theoretical foundations and well-established hardness against both classical and quantum attacks. In this thesis, we explore several directions of lattice based cryptology and quantum algorithms.

On the construction side, we propose two compact encryption schemes based on the …

Bias, Structure, And Inference In Applied Network Analysis, Anna Vasenina

Dartmouth College Ph.D Dissertations

This dissertation develops mathematical and statistical methods for extracting reliable information from network data across biological applications, with an emphasis on understanding what observed network structure can and cannot resolve. The first study leverages protein–protein interaction network topology in the c-di-GMP signaling system of Pseudomonas fluorescens, showing that node centrality measures accurately classify protein domain types and that physical interaction structure contributes statistically significant predictive power for biofilm formation phenotypes across nearly 200 environments, while gene expression does not. The second study examines sampling bias in lemur-plant trophic interaction networks in Madagascar, demonstrating that differential detection of diurnal versus …

A Professional Development Course On Data-Driven Dynamical Systems At A Primarily Undergraduate Institution: Part A - Scientific Content, Alessandro M. Selvitella, Jeffrey R. Anderson

CODEE Journal

In the age of data-driven decision making, ordinary differential equations (ODEs) remain a powerful and interpretable framework for modeling dynamic processes, especially when integrated with modern tools from statistical learning and data-driven dynamical systems. Yet, general undergraduate and graduate curricula do not typically address key opportunities in data-driven dynamical systems.

This first paper in a series focuses on the mathematical and methodological core of a professional development course first developed in the academic year 2025-2026 at a Primarily Undergraduate Institution, Purdue University Fort Wayne. The curriculum developed in this course emphasized how regression, regularization, and sparse identification can be used …

Some Results In Maximal Pattern Complexity, Casey Schlortt

Electronic Theses and Dissertations

For a finite alphabet 𝒜 and a sequence 𝑥 ∈ 𝒜^ℕ_⊬ , Kamae and Zamboni combined the ideas of block complexity and topological sequence entropy to define the maximal pattern complexity, 𝑝^∗_𝑛 (𝑥). They defined an aperiodic sequence 𝑥 over two letters as pattern Sturmian if it had the lowest possible maximal pattern complexity, 2𝑛. Later, Kamae and Rao extended their definition of pattern Sturmian sequences to be sequences over ℓ ≥ 2 letters which are not periodic by projection and have maximal pattern complexity ℓ𝑛.

This dissertation answers a question posed by Kamae and Zamboni …

Beyond The Best Fit: Fitting Sir-Style Models To Data While Prioritizing Biological Meaning, Meredith L. Greer

CODEE Journal

Many students find comfort in mathematics because math classes have been a place where they can find the “right answer” to exercises. Modeling courses typically emphasize more nuance, teaching students to try modeling approaches, compare back with real-world mechanisms and data, and then refine their models, in an ongoing cycle. One topic, however, can cause students to quickly revert into “right answer” mode: fitting a model to data. Phrases such as best fit and minimize the distance suggest there is one optimal solution that can be determined by an algorithm, and these algorithms typically have no relationship to the biology …

Uniform Stability Of Katyusha In Strongly-Convex Settings, Don Li

University Honors Theses

Acceleration of convergence and reduction of variance constitute a trade-off in the design of stochastic optimization machine learning algorithms. Katyusha was introduced to address this trade-off, synthesizing Nesterov Accelerated Gradient (NAG) and Stochastic Variance-Reduced Gradient (SVRG) into a single first-order optimizer with promising empirical performance. However, the generalization properties of Katyusha remain largely unexplored. We conjecture that, in the smooth quadratic regime (i.e., under assumptions of strong convexity and smoothness of the loss function, and boundedness of gradients), Katyusha is uniformly stable in the sense of Bousquet and Elisseeff. Instantiating our framework for NAG, we extend the use of Lyapunov …

The Method Of Periodic Averaging Applied To Reduced Coupled Mode Theory Models For Fiber Laser Amplifiers, Rebecca Nicole Bryant

Dissertations and Theses

Fiber laser amplifier (FLA) models are often implemented without rigorous mathematical justification or thorough numerical validation. Without a proper theoretical basis for assumptions and approximations, or a technical analysis of model performance, there is significant uncertainty about the limitations of any given reduced model and its suitability for an application. This research aims to address the lack of comprehensive assessment of FLA models by directly comparing distinct models and recommending a mathematical alternative to replace heuristic model-reduction techniques. The work in this dissertation is divided into two projects: a comparative study that uses existing FLA models to assess the validity …

Course Portfolio: Elements Of Physics Phys 151, Evan A. Rich

UNL Faculty Course Portfolios

This course portfolio documents the instructional design, teaching methods, and ongoing assessment efforts for PHYS 151: Elements of Physics, an algebra-based introductory physics course at the University of Nebraska-Lincoln. The course serves a broad undergraduate population, including architecture, construction management, and life science majors. The portfolio describes the teaching framework that integrates pre-lecture video preparation, active in-class engagement through iClicker questions, and collaborative weekly recitation sections, all unified around a structured six-step problem-solving approach. A central concern of the course is building students’ self-efficacy in physics, particularly among those with math anxiety or limited preparation. Two assessments are reported: a …

Koba-Nielsen Local Zeta Functions, Convex Subsets, And Generalized Selberg-Mehta-Macdonald And Dotsenko-Fateev-Like Integrals, Willem Veys, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

The Koba-Nielsen local zeta functions are integrals depending on several complex parameters, used to regularize the Koba-Nielsen string amplitudes. These integrals are convergent and admit meromorphic continuations in the complex parameters. In the original case, the integration is carried out on the n-dimensional Euclidean space. In this work, the integration is over a variety of (bounded or unbounded) convex subsets; the resulting integrals also admit meromorphic continuations in the complex parameters. We describe the meromorphic continuation's polar locus explicitly, using the technique of embedded resolution. This result can be reinterpreted as saying that the meromorphic continuations are weighted sums of …

Quantitatively Hyper-Positive Real Rational Functions Iii, Daniel Alpay, Izchak Lewkowicz

Mathematics, Physics, and Computer Science Faculty Articles and Research

Hyper-Positive Real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related through nested inclusions, are introduced. Structurally, this family of functions turns out to be matrix-convex and closed under inversion. A state-space characterization of these functions through a corresponding Kalman-Yakubovich-Popov Lemma, is given. Technically, the classical Linear Matrix Inclusions, associated with passive systems, are here substituted by Quadratic Matrix Inclusions.

Obstructions To Some Injective Oriented Colourings, Russell J. Campbell, Nancy E. Clarke, Gary Macgillivray

Theory & Applications of Graphs

Each of several possible definitions of local injectivity for a homomorphism of an oriented graph $G$ to an oriented graph $H$ leads to an injective oriented colouring problem. For each case in which such a problem is solvable in polynomial time, we identify a set $\mathcal{F}$ of oriented graphs such that an oriented graph $G$ has an injective oriented colouring with the given number of colours if and only if there is no $F \in \mathcal{F}$ for which there is a locally-injective homomorphism of $F$ to $G$.

The Connected Vertex Cover In Graphs, Kamran Mirasheh, Elham Mirashe, Ebrahim Vatandoost

Theory & Applications of Graphs

This paper presents tight bounds and characterizations for the vertex cover number and the connected vertex cover number of graphs. In particular, we identify all graphs for which βc(G) = |V (G)| − 1, proving that these are exactly the cycles and complete graphs. The analysis employs tools such as the degree matrix and the Rayleigh quotient to derive new and sharp upper bounds.

The $K$-Total Bondage Number Of A Graph, Jean-Pierre Appel, Gabrielle Fischberg, Kyle Kelley, Nathan B. Shank, Eliel Sosis

Theory & Applications of Graphs

Let \(G=(V,E)\) be a connected, finite undirected graph. A set \(S \subseteq V\) is said to be a total dominating set of \(G\) if every vertex in \(V\) is adjacent to some vertex in \(S\). The total domination number, \(\gamma_{t}(G)\), is the minimum cardinality of a total dominating set in \(G\). We define the \(k\)-total bondage of $G$ to be the minimum number of edges to remove from \(G\) so that the resulting graph has a total domination number at least \(k\) more than \(\gamma_{t}(G)\). In this work we establish general properties of \(k\)-total bondage and find exact values for …

Hyper Face-Magic Graphs, Ross Belgram, Donald Mcginn

Theory & Applications of Graphs

For a planar graph G of order n, let F(G) be the set of all faces of G embedded into R 2 , including the exterior face. A bijective vertex labeling f : V (G) → {1, 2, ..., n} induces a face labeling f ∗ : F(G) → N defined by setting f ∗ (F) equal to the sum of all labels of the boundary vertices of F. The graph G is said to be hyper face-magic if there exists a vertex labeling whose induced face labeling is constant. In this paper, we state properties of hyper face-magic graphs …

The Malaugh Operations And The Quadratic Invariant Gaps Of $\Si_4^C$, Forrest M. Hilton

ETDs from 2020-2029

Connected Julia sets of polynomials generally correspond to laminations, sets of chords of the unit disc that reflect the dynamics of the Julia set. If the circle is measured in revolutions and the polynomials studied are of degree $d$, then the dynamics on the lamination is given by the covering map $\sigma_d(t) := td \pmod 1$ where chords are mapped by their end points. Every lamination has at least one laminational invariant set, which is loosely an invariant complementary component of the lamination. That set has a significant impact on the shape of the Julia set. James Malaugh showed how …

On The Fractional Laplacian Type Operator, Maysam Abdulnaser Zain

Thesis/ Dissertation Defenses

In this thesis, we study analytical structures arising from Dunkl theory and their applications to harmonic analysis and fractional Laplacian operators. Dunkl operators are differential-difference operators associated with finite reflection groups, providing a natural generalization of the classical Fourier analysis through the introduction of root systems and multiplicity functions. Within this framework, several classical transforms appear as special cases of the (k,a)-generalized Fourier transform. We study the generalized Fourier transform, its kernel, and the associated translation operator and convolution structures. Using these tools, we construct the corresponding heat kernel and analyze the associated heat semigroup. Our main contribution concerns the …

The Impact Of Evolution And Strong Allee Effects On The Dynamics Of A Discrete-Time Predator-Prey System, Neerob Basak

Doctoral Dissertations

This dissertation investigates the dynamics of discrete-time predator-prey systems, focusing on both evolutionary responses and ecological interactions. The first part of this dissertation, in Chapters 2 and 3, explores how evolutionary processes, particularly the development of resistance to toxicants in predators, influence the persistence and stability of predator-prey populations. In this part, we extend the predator-prey model developed in Ackleh et al., 2019 to incorporate the evolution of a predator's resistance to toxicant effects. We consider three cases: (1) lethal effects, where the toxicant directly influences the predator's survival; (2) sublethal effects, where the toxicant impacts the predator's fecundity, and …

The Interplay Of Seasonality, Evolution, And Density-Dependence In Discrete-Time Predator-Prey Dynamics, Narendra Pant

Doctoral Dissertations

We extend the discrete-time mathematical models developed in (Ackleh et al., 2019) and (Ackleh et al., 2024) to account for seasonal prey reproduction and build a class of discrete-time predator-prey seasonal models. Each model distinguishes between breeding and non-breeding seasons, representing prey reproduction as a periodic function of period 2. Altogether, three different models are analyzed. In the first part, we extend the predator-prey model from (Ackleh et al., 2019) to incorporate seasonality. We study the resulting dynamics and show that when the inherent reproduction number of the prey and the invasion reproduction number of the predator are larger than …

Generating Live Heatmaps Of Edr Data Through A Spatiotemporal Weighting, Joel T. Williams, C. Sean Bohun, Alberto Fornaci, Michael R. Lindstrom

School of Mathematical & Statistical Sciences Faculty Publications

This paper introduces a novel method for generating live heatmaps of eddy dissipation rate (EDR) data through a spatiotemporal weighting designed to enhance turbulence visualization in aviation. As more flight data become available, approaches relying solely on in-flight EDR measurements have the potential to accurately nowcast and visualize turbulence with low computational cost. The proposed method significantly improves the turbulence visualization capabilities of common commercial aircraft. This is particularly valuable for pilot decision-making and trip planning, enhancing flight safety and operational efficiency. This approach also incorporates an innovative uncertainty threshold, which refrains from predicting when there are insufficient data, thereby …

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.

Constructing Orthonormal Bases With The Residuals Of Successive Approximations, An Introduction To Multiresolution Analysis, Elijah J. Guptill

Master's Theses

Wavelets and wavelet analysis are used in the study of signal processing, quantum field theory, functional analysis, multifractal analysis, and various other areas of mathematics. Multiresolution analysis provides a framework for building a wavelet basis of $\mathcal{L}^{2}(\mathbb{R})$ from a scaling function $\phi$, whose dyadic dilations and translations, $\{2^{j /2}\phi(2^{j}x-k):j,k\in \mathbb{Z}\}$, approximate $\mathcal{L}^{2}(\mathbb{R})$. One of the key properties of  $\phi$ is that it must satisfy $\phi(x)=\sum_{k\in \mathbb{Z}}{p_{k}2^{j /2}\phi(2^{j}x-k)}$ with respect to the norm on $\mathcal{L}^{2}(\mathbb{R})$. This equation is called a two-scale difference equation. Such equations enforce a regularity on the ordinary generating function $2^{-1 /2}\sum_{k\in \mathbb{Z}}{p_{k}z^{k}}$, known as the quadrature condition. …

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 …

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) + Σ_j=1^N α_jδ_pj on bounded Lipschitz domains Ω ⊂ ℝ² with homogeneous Dirichlet boundary condition, and on a flat torus 𝕋², where α_j is positive for the Dirichlet setting and α_j 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 …

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 …

Introduction To Mathematical Analysis Ii, Beatriz Lafferriere, Gerardo Lafferriere, Mau Nam Nguyen

PDXOpen: Open Educational Resources

These lecture notes complement the book Introduction to Mathematical Analysis I, Third Edition, with sections on integration, numerical series, series of functions, and selected advanced topics. Together, both volumes support a one semester or two-quarter course on introductory mathematical analysis.

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Behind The Screen: A Comprehensive Framework For Digital Work Metrics And Data Integration, F. Demaria, A. Papana Dagiasis, M. Cavicchioli, T. Fabbri

Mathematics and Statistics Faculty Publications

The digital transformation and the subsequent datafication of work generate rich electronic traces that can be transformed into actionable insights through modern analytics. In this context, this study proposes a data-driven framework that leverages sidClustering and unsupervised Random Forest (RF) for clustering and feature selection, constructs composite indicators via multiple aggregation strategies, and employs visual tools to enhance the interpretability of results. A key feature of the framework is the integration of two data sources: click metadata from Microsoft 365 and employee attitudes measured through a questionnaire. This integration enables the analysis of digital work behavior (DWB) in relation to …