A Copula-Based Framework For Multivariate Count Time Series With Mixed Marginal Distributions,
2026
Grand Valley State University
A Copula-Based Framework For Multivariate Count Time Series With Mixed Marginal Distributions, Dimuthu Fernando, Yuxin Wen, Wimarsha Jayanetti
Engineering Faculty Articles and Research
We developed a class of multivariate integer-valued time series models using copula theory. Each count time series is modeled as a Markov chain, with serial dependence characterized through copula-based transition probabilities for Poisson and negative binomial marginals. Cross-sectional dependence is modeled via a trivariate Gaussian or a “t-copula”, allowing for both positive and negative correlations and providing a flexible dependence structure. Model parameters are estimated using likelihood-based inference, where the trivariate Gaussian or t-copula integrals are evaluated through standard randomized Monte Carlo methods. Simulation results, along with an analysis of annual counts of major hurricanes (Category 3+) across the North …
Constructing Orthonormal Bases With The Residuals Of Successive Approximations, An Introduction To Multiresolution Analysis,
2026
California Polytechnic State University, San Luis Obispo
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. …
A Symbolic Model Of Proof Acquisition In Act-R,
2026
University of Denver
A Symbolic Model Of Proof Acquisition In Act-R, Beckett Morris, Kerstin Haring
DU Undergraduate Research Journal Archive
Learning to construct mathematical proofs—formal arguments demonstrating the truth of a mathematical statement using logical deductions and previously established facts—is one of the most challenging skills in STEM education. This research aims to build the foundations for a symbolic cognitive model, using the ACT-R cognitive architecture and implementing in Python with the pyactr package, to explore how different proof strategies can be thought through with only symbols and rules. The model observes simple proofs, and its abilities are assessed based on its generalization capabilities, efficiency, and error patterns. By developing and analyzing such a model, this research provides new insights …
The Isoperimetric Inequality And Wirtinger’S Inequality,
2026
University of Mississippi Main Campus
The Isoperimetric Inequality And Wirtinger’S Inequality, Mason Neal
Honors Theses
In this thesis, we present Hurwitz’s proof of the Isoperimetric Inequality, which roughly states that the area enclosed by a simple closed curve is always less than or equal to the area of a circle with the same perimeter. Hurwitz’s proof relies on Wirtinger’s Inequality. We survey results about periodic functions and Fourier series, and we use them to provide a proof of Wirtinger’s Inequality. We then give a new proof of a variant of Wirtinger’s Inequality due to Alzer and generalize this variant to higher powers.
A Two-Phase Perspective On A Related-Rates Paradox,
2026
Northern Illinois University
A Two-Phase Perspective On A Related-Rates Paradox, Charlie Vazquez Acosta
Honors Capstones
Related-rates problems are a standard topic in first-year calculus and have appeared in textbooks for over 150 years. These problems are used to teach implicit differentiation and the relationship between changing quantities. Common examples include the falling ladder, the fishing bobber, the melting snowball, and the leaking conical tank. In each of these problems, a quantity is changing at a constant rate, and students are asked to find the rate of change of another related quantity. While the computations themselves are usually straightforward, the standard models lead to unrealistic results near the end of the motion. For example, the falling …
Leveraging Information Theory And Ecological Network Analysis To Monitor Communication Networks In A Student Aerospace Team,
2026
Embry-Riddle Aeronautical University
Leveraging Information Theory And Ecological Network Analysis To Monitor Communication Networks In A Student Aerospace Team, Christine Sessions
Doctoral Dissertations and Master's Theses
Effective communication is a critical component of successful collaboration in group projects and team settings. However, systematically tracking and analyzing team communications can be challenging, especially in complex, multi-member teams such as those found in the aerospace industry. This paper explores an information-theoretic approach that leverages encoding techniques and graph theory to analyze communication networks within a university’s multi-year, student-led cubesat design project (Project COMET). By utilizing Shannon Entropy as a measure of information flow, encoding communication patterns, and analyzing Ecological Network Analysis parameters, this research aims to understand how an Embry-Riddle Aeronautical University student project team evolves over the …
Primitive Pythagorean Triples In Lean And Reduction Modulo Odd Prime Powers,
2026
University of Arkansas, Fayetteville
Primitive Pythagorean Triples In Lean And Reduction Modulo Odd Prime Powers, Luke Biddle
Mathematical Sciences Undergraduate Honors Theses
Primitive Pythagorean triples (PPTs) are (a,b,c) triples that satisfy the Pythagorean theorem and share no other common factors outside of 1. This project examines these PPTs reduction modulo odd prime powers by combining proof writing and number-theoretical analysis with the process of verification and formalization in the Lean proof coding language. Using the parameterization of PPTs generated by using the unit circle with additional conditions, we investigate how these triples behave modulo for odd primes , with emphasis on counting the number of elements in the set of PPTs (a,b,c) modulo pn . By using cases based on initial …
Decision Making For Large-Scale Problems Under Uncertainty And Conflict,
2026
Clemson University
Decision Making For Large-Scale Problems Under Uncertainty And Conflict, Benjamin J. Hamlin
All Dissertations
Large-scale decision-making problems appear in many areas including long-range forecasting such as energy generation forecasting. Many such problems are subject to conflicting objectives and uncertain data, and can be modeled as linear optimization problems. We study novel theoretical results and algorithms for large-scale linear decision problems under conflict and uncertainty. First, we propose a parametric Benders decomposition algorithm for solving large-scale linear optimization problems with multiple objectives or deterministically uncertain objectives. Second, we extend the parametric Benders decomposition to a multi-stage setting, developing a parametric stochastic dual dynamic programming algorithm, which enables decision-making when conflicts and uncertainty have planning impacts …
A New Approach To Generate Combinatorial Patterns In Logical Analysis Of Data And Its Application To Predict College Retention,
2026
Florida Institute of Technology
A New Approach To Generate Combinatorial Patterns In Logical Analysis Of Data And Its Application To Predict College Retention, Salihah Ahmed E. Jaafari
Theses and Dissertations
Student retention and degree completion remain central challenges for higher-education institutions, with significant implications for student success, institutional effectiveness, and public accountability. While advances in predictive analytics have enabled earlier identification of students at risk of withdrawal, many commonly used machine learning approaches suffer from limited interpretability, constraining their practical usefulness for advising, intervention, and policy decision making. This dissertation addresses the problem of predicting student persistence by developing and evaluating optimization based, interpretable classification models within the Logical Analysis of Data (LAD) framework. Building on existing LAD formulations, this research introduces two novel pattern generation models, the Best Term …
Examining Student Practices In A Technology-Mediated Math Classroom,
2026
California State University, San Bernardino
Examining Student Practices In A Technology-Mediated Math Classroom, Bradley T. Dodd
Electronic Theses, Projects, and Dissertations
It is important for math educators to make sense of student thinking in the classroom. Without opportunities to practice this skill math educators struggle to improve, particularly when students are engaging in mathematics using technology. As such, there is a need for video artifacts of students engaging with mathematics using technology for use in professional development activities (Lovett 2020). In accordance with Lovett et al.'s (2020) design principles for examining student practices in a technology-mediated environment, I carried out a study to determine whether these artifacts of student work could be created working with college undergraduates as participants. Students engaged …
Fractsynth: Exploring Glitch Timbres With Chaos Theory,
2026
Grand Prairie Fine Arts Academy
Fractsynth: Exploring Glitch Timbres With Chaos Theory, Aidan Roach
The Transdisciplinary STEAM+ Journal
In this paper, I explore how chaos theory can be used to design a new kind of synthesizer with the primary focus of producing glitchy, unpredictable sounds. Glitch music embraces abstract sound design, malfunctioning electronics, and randomness as the main compositional elements. However, most synthesizers rely on stable, repetitive oscillators that often sound too controlled. To challenge this, I developed FractSynth, a real-time synthesizer that uses chaotic attractors–including the Logistic Map, Henon Map, and Lorenz System–as modulation sources for frequency, amplitude, and tone. The software also features real-time Lyapunov Exponent Tracking, which gives users a direct visual of how …
Interactions Of Dance And Mathematics: A Closer Look At Mathematical Sequences As Scores For Choreography From A Choreographic Lens,
2026
Missouri State University - Springfield
Interactions Of Dance And Mathematics: A Closer Look At Mathematical Sequences As Scores For Choreography From A Choreographic Lens, Caroline Wolfe
The Transdisciplinary STEAM+ Journal
This paper investigates the embodiment of infinite mathematical sequences through concert contemporary dance, examining how choreography can serve both as an artistic and analytical tool for exploring numerical patterns. Grounded in interdisciplinary literature on mathematical visualization in choreography, the study centers on two original choreographic works presented and performed at Missouri State University: Golden Ratio Sequence (Spring 2025), which maps the Fibonacci sequence and the natural applications of the Golden Ratio onto a spiral floor pattern, and Tetrahedral Numbers (Fall 2024), which employs an accumulation score to embody three-dimensional number growth through layered movement motifs and body created tetrahedra. The …
Unique Combinations Of Packing Integer Squares,
2026
Fort Hays State University
Unique Combinations Of Packing Integer Squares, Keith M. Dreiling, Austin Leanna, William Mooney
SACAD: Scholarly Activities
This research investigates a function, informally named WAK(x), that describes the number of ways to divide an integer square into integer subsquares counting only the list of parts. Previous research has shown values up to 28, though finding these values is computationally complex and requires a long runtime using computer algorithms. We attempt to find patterns in the values and many aspects of the values, hoping to find a general solution. We are unsure if a solution exists, but we have ideas for how to move forward in finding a solution.
Counting Hamiltonian Cycles In Quartic Circulant Graphs,
2026
Pepperdine University
Counting Hamiltonian Cycles In Quartic Circulant Graphs, Allison Hilliard
Seaver College Research And Scholarly Achievement Symposium
We consider the problem of counting Hamiltonian cycles in circulant graphs $C^K_n$ where $n$ is the number of vertices and $K$ is a set containing elements that correspond to the allowed edges in the circulant graphs. After sorting the cycles by a topological invariant called the winding number, we use a modified transfer matrix method to convert local data into global structures. The result is a generating function that counts the number of Hamiltonian cycles in a circulant graph with $n$ vertices. The results for $K=\{1,2\}$ and $K=\{1,3\}$ have been found by previous authors. We focus on the case where …
On Links Between A Theorem Of Schoenberg, Rohlin Decompositions Of Measures, The Bochner-Minlos Theorem And The Fock Space,
2026
Chapman University
On Links Between A Theorem Of Schoenberg, Rohlin Decompositions Of Measures, The Bochner-Minlos Theorem And The Fock Space, Daniel Alpay, Paula Cerejeiras, Palle Jorgensen, Uwe Kaehler
Mathematics, Physics, and Computer Science Faculty Articles and Research
The main goal of this paper is to gain new results in stochastics by drawing on, and combining, different areas that are normally not considered to be related. Thus, in this paper we extend the previous class of Gaussian-like functions ML which will allow for future generalized stochastic processes in infinite dimensional analysis. We show that an approach similar to the one by the classical Bochner-Minlos theorem for the white-noise case can be achieved by using Gaussian-like functions belonging to a large family -the MLr classes (0 < r ≤∞). We show how Schoenberg’s theorem for positive definite functions on a Hilbert space allows to go beyond the classical setting of Bochner-Milnos theorem. Furthermore, we show that the application of the Rohlin’s disintegration theorem allows for a decomposition of the associated probability measures , see Theorems 3.2 and 4.3. We end this paper with several important examples of functions in these classes MLr and provide some interesting counterexamples, e.g. Theorem 7.4, to get a …
Automating Cardiff Model Data Capture In Emergency Departments: Ambient Nlp Integration With Oracle-Cerner Fhir Systems,
2026
Southern Methodist University
Automating Cardiff Model Data Capture In Emergency Departments: Ambient Nlp Integration With Oracle-Cerner Fhir Systems, Simi Augustine, Marco A. Lopez, Jacquelyn Cheun, Chris Papesh
SMU Data Science Review
Violence and overdose events in Las Vegas occur at rates above the national average, with fewer than half of violent injuries reported to law enforcement [2,7]. The Cardiff Model offers a proven framework for standardized data collection and sharing between hospitals and public safety partners, yet many implementations still rely on manual entry. We propose an ambient triage pipeline integrated with Oracle-Cerner electronic health record systems to listen to nurse–patient dialogue, convert speech to text, extract Cardiff fields, and write standards-based FHIR Bundles for analytics. Using SMART on FHIR standards and Cerner Millennium APIs, the study evaluates whether ambient capture …
Numerals And Other Means Of Expressing Plurality In Language And Thought: A Developmental Perspective Across Cultures.,
2026
I.I.S. Fantini. Vergato (Bologna - Italy)
Numerals And Other Means Of Expressing Plurality In Language And Thought: A Developmental Perspective Across Cultures., Giovanni Giuseppe G.G. Nicosia Prof.
Numeracy
Several ancient languages use linguistic structures to differentiate between singular, dual, and plural forms that are used when one, two, or many objects are referenced. (Some languages go further, adding a trial form to differentiate two from three.) In many modern languages, numerals are used to convey precise number. After reviewing a range of ways languages express number (including the interesting case of Pirahã which does not express precise number), the paper concludes with a proposed developmental path for the expression of quantity in languages.
Minimal Supersolution Of Bsdes Driven By Continuous Martingales In A General Filtration,
2026
Cadi Ayyad University (UCA), National School of Applied Sciences of Marrakech (ENSA-M), BP 575, Avenue Abdelkrim Khattabi, 40000, Guéliz, Marrakech, Morocco
Minimal Supersolution Of Bsdes Driven By Continuous Martingales In A General Filtration, Badr Elmansouri, Mohamed El Otmani
Journal of Stochastic Analysis
In this paper, we study minimal supersolutions of backward stochastic differential equations (BSDEs) driven by a continuous local martingale in a general filtration. We establish existence, uniqueness, and stability results under various mild conditions on the terminal value and the generator. Additionally, we explore the connection between the concept of non-linear expectation and minimal supersolutions, emphasizing the specific properties that are relevant to our framework. We also prove a general monotonic limit theorem and apply this result to determine the smallest constrained supersolution of a BSDE with a possibly non-convex constraint.
A Virtual Community Math Circle,
2026
Santa Barbara Math Ellipse
A Virtual Community Math Circle, Skona Brittain, Sayonita Ghosh Hajra, Steve Heller, Daniel Hodgins, Peter Petto, Gabriella Pinter, Lauren Rose, A. Gwinn Royal, Asmita Sodhi
Journal of Math Circles
The Julia Robinson Mathematics Festival (JRMF) Community Math Circle is free, volunteer-run, and online. We collaborate with JRMF and use their activities in our events. Started during the pandemic, the Community Math Circle continues to thrive. We have about 40 participants attending every month, typically kids aged 6 to 13, teachers, facilitators, and other adults. This article describes how our event is organized, planned, and executed, and how we train facilitators. We will also offer reflections on our successes and challenges.
Effective Wordle Heuristics,
2026
Loyola University Chicago
Effective Wordle Heuristics, Ronald I. Greenberg
Computer Science: Faculty Publications and Other Works
While previous researchers have performed an exhaustive search to determine an optimal Wordle strategy, that computation is very time consuming and produced a strategy using words that are unfamiliar to most people. With Wordle solutions being gradually eliminated (with a new puzzle each day and no reuse), an improved strategy could be generated each day, but the computation time makes a daily exhaustive search impractical. This paper shows that simple heuristics allow for fast generation of effective strategies and that little is lost by guessing only words that are possible solution words rather than more obscure words.
