Numerical Analysis and Computation Commons^™

Phenological Overlap In Obligate Plant-Pollinator Mutualism, Austin J. Carlson

2026 Spring Honors Capstones Projects

Plant-pollinator mutualisms require temporal overlap between flowering and pollinator activity, so climate-driven timing shifts can weaken the interaction and, in severe cases, destabilize the system. This work investigates how reduced overlap affects persistence in an obligate plant-pollinator pair using a coupled differential equation model in which a phenological overlap factor scales the saturating mutualistic benefit. Simplification with a constant overlap enables closed-form equilibrium and stability analysis, revealing that below a critical overlap threshold, coexistence is no longer maintained. Rescaling reduces the parameter space from ten quantities to seven dimensionless groups, and sensitivity analysis identifies the degree of species dependence and …

Using Ai To Analyze Survey Data, Sara Martucci

Open Educational Resources

This assignment in Methodology in Sociology/Criminology engages students in the full research process by guiding them through variable selection, data analysis, interpretation, and critical reflection on AI-assisted decision-making. Using a class-generated survey dataset (or an existing dataset), students develop a research question, identify independent and dependent variables, and formulate a hypothesis. They then compare their selections with those suggested by an AI tool, analyzing differences in reasoning and variable choice. Through SPSS, students generate frequency tables, charts, and scatterplots to examine relationships between variables, including potential intervening factors. The assignment culminates in a group presentation and reflective analysis on the …

Cami: A Counselor Agent Supporting Motivational Interviewing Through State Inference And Topic Exploration, Yizhe Yang, Palakorn Achananuparp, Heyan Huang, Jing Jiang, Phey Ling Kit, Nicholas Gabriel Lim, Cameron Shi Ern Tan, Ee-Peng Lim

Research Collection School Of Computing and Information Systems

Conversational counselor agents have become essential tools for addressing the rising demand for scalable and accessible mental health support. This paper introduces CAMI, a novel automated counselor agent grounded in Motivational Interviewing (MI) – a client-centered counseling approach designed to address ambivalence and facilitate behavior change. CAMI employs a novel STAR framework, consisting of client’s state inference, motivation topic exploration, and response generation modules, leveraging large language models (LLMs). These components work together to evoke change talk, aligning with MI principles and improving counseling outcomes for diverse clients. We evaluate CAMI’s performance through both automated and expert evaluations, utilizing simulated …

Decoding The Algorithm: The Mathematics Behind Tiktok’S Short-Form Content Success, Ashley N. Lynch

Honors Scholar Theses

Within the realm of social networks, TikTok has become the central hub for short-form video content. The network’s unique ability to capture individual preferences using predictive analytics has greatly contributed to its massive success, allowing the company to optimize its performance and content personalization. In an age where digital media have such a significant influence on society, it is essential that users develop an understanding of how social network algorithms function to make more informed online decisions. Although TikTok’s technological system is primarily undisclosed, the platform certifiably leverages several key mathematical principles within its algorithm to achieve its core goals …

Physics Embedded Neural Network: A Novel Data-Free Numerical Method For Solving Computational Physics Problems, Pawan Gaire

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

A novel approach for solving partial differential equations (PDEs) using neural networks for scientific computing is introduced. The proposed approach, referred to as physics-embedded neural network (PENN), features a unique architecture that incorporates the PDE and boundary conditions information directly within the final fully-connected layer of the feed-forward neural network (NN). The key aspect of PENN is the parallel numerical embedding of a differential equation associated with physical problems within the activation function of the network’s final layer. This integration leads to a new class of computational solvers competitive with classical methods like the Finite Element Method (FEM) and capable …

Using Permutation Groups To Identify Families Of Capacity Achieving Codes, Daniel Welchons

Department of Mathematics: Dissertations, Theses, and Student Research

When communicating over a noisy channel, the probability of message interference sets a maximum possible transmission rate known as the channel capacity. Any family of codes which have rates converging to the channel capacity and arbitrarily low probability of decoding failure is called capacity achieving. Such codes have been known to exist since the birth of information theory, but are difficult to find explicitly. It has recently been shown that the permutation groups of a family of codes can be used to show that the family is capacity achieving on the q-ary erasure channel.

This thesis seeks to apply the …

Using Permutation Groups To Identify Family Of Capacity Achieving Codes, Daniel Joseph Welchons

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

When communicating over a noisy channel, the probability of message interference sets a maximum possible transmission rate known as the channel capacity. Any family of codes which have rates converging to the channel capacity and arbitrarily low probability of decoding failure is called capacity achieving. Such codes have been known to exist since the birth of information theory but are difficult to find explicitly. It has recently been shown that the permutation groups of a family of codes can be used to show that the family is capacity achieving on the q-ary erasure channel.

This this thesis seeks to …

Towards Advancing Streamflow And Peak Flow Prediction With Machine Learning: Identifying Infrastructure At Risk, Sudan Pokharel

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

Due to climate change and its impact, the need for adaptive strategies for natural disaster mitigation and resource management has never been more urgent. Central to this is water resource management, which is essential for sustainable human activities, ecological balance, and the mitigation of natural hazards like floods. Streamflow is a crucial element of water resource management and plays a vital role in planning and building water infrastructure, implementing emergency response plans, supporting flood mitigation initiatives, and regulating agricultural and industrial use. However, accurate prediction of streamflow still remains a challenge due to the complex non-linear and non-stationary interaction between …

Quantitative Runtime Monitoring Of Ethereum Transaction Attacks, Xinyao Xu, Ziyu Mao, Jianzhong Su, Xingwei Lin, David Basin, Jun Sun, Jingyi Wang

Research Collection School Of Computing and Information Systems

The rapid growth of decentralized applications, while revolutionizing financial transactions, has created an attractive target for malicious attacks. Existing approaches to detecting attacks often rely on predefined rules or simplistic and overly-specialized models, which lack the flexibility to handle the wide spectrum of diverse and dynamically changing attack types. To address this challenge, we present a general and extensible framework, MoE (Monitoring Ethereum), that leverages runtime verification to detect a wide range of attacks on Ethereum. MoE features an expressive attack modeling language, based on Metric First-order Temporal Logic (MFOTL), that can formalize a wide range of attacks. We integrate …

Project Title: Maximizing The Volume Of A Cardboard Box To Save Trees– An Application Of Polynomial Functions To Address Global Issues [Mathematics], Lucie Mingla

Open Educational Resources

MAT 115 College Algebra & Trigonometry/Precalculus

Project Title: Maximizing the Volume of a Cardboard Box to Save Trees– An Application of Polynomial Functions to Address Global Issues

Reflective Narrative:

This project was inspired by my participation in the "Designing and Implementation of STEM Co-Curricular Activities" CTL seminar in Spring 2023. I am grateful to Drs. Bukurie Gjoci, Daniel Gertner, Ingrid Veras, and Midas Tsai, along with fellow participants, for their invaluable feedback that helped shape its development. The project was implemented in two College Algebra and Trigonometry courses. I participated in two seminars to further develop this project. The Community …

Mathematical Modelling Of Hybrid Photonic Structures For Holographic Sensors, Jack Lyons

Doctoral

This thesis outlines a mathematical framework for modelling the formation of holographic gratings in hybrid photopolymer based nanocomposites with the aim of optimising their holographic recording properties for optical sensing applications. Thus, the second aim of the work is to model the change in optical properties of the grating in response to exposure to a target analyte. This work has been a collaborative research project between the School of Mathematics & Statistics at Technological University Dublin and the Centre for Industrial and Engineering Optics that have done extensive experimental work with holographic gratings recorded in photopolymer materials.

In recent years, …

Question-Attentive Review-Level Explanation For Neural Rating Regression, Trung Hoang Le, Hady Wirawan Lauw

Research Collection School Of Computing and Information Systems

Recommendation explanations help to improve their acceptance by end users. Explanations come in many different forms. One that is of interest here is presenting an existing review of the recommended item as the explanation. The challenge is in selecting a suitable review, which is customarily addressed by assessing the relative importance or “attention” of each review to the recommendation objective. Our focus is improving review-level explanation by leveraging additional information in the form of questions and answers (QA). The proposed framework employs QA in an attention mechanism that aligns reviews to various QAs of an item and assesses their contribution …

Production Box Cost Estimating Relationships For Dod Avionics, Carla J. Cisneros, Edward D. White, Brandon M. Lucas, Jonathan D. Ritschel, Robert D. Fass, Shawn M. Valentine

Faculty Publications

The authors use historical information obtained from the Cost Assessment Data Enterprise to estimate recurring production unit cost for DoD avionics via cost estimating relationships (CERs). The specific modeled responses include mean unit cost, median unit cost, and the 100th production unit cost (T100) utilizing learning curve theory. For T100, the authors adopt both a multiplicative and an additive error for CER comparison. Recommended CERs consist of the mean unit cost and the T100 utilizing a multiplicative error. Moreover, results reveal that weight has a significant effect on cost as well as a potential underaccounting of real price change or …

Conjugations Of Unitary Operators, I, Javad Mashreghi, Mraek Ptak, William T. Ross

Department of Math & Statistics Faculty Publications

If U is a unitary operator on a separable complex Hilbert space H, an application of the spectral theorem says there is a conjugation C on H (an antilinear, involutive isometry on H) for which CUC= U*. In this paper, we fix a unitary operator U and describe all of the conjugations C which satisfy this property. As a consequence of our results, we show that a subspace is hyperinvariant for U if and only if it is invariant for any conjugation C for which CUC = U*.

Normrank Correlations For Testing Associations And For Use In Latent Variable Models, Daniel B. Wright

Educational Psychology, Leadership, and Higher Education Faculty Research

Pearson’s correlation is widely used to test for an association between two variables and also forms the basis of several multivariate statistical procedures including many latent variable models. Spearman’s p is a popular alternative. These procedures are compared with ranking the data and then applying the inverse normal transformation, or for short the normrank transformation. Using the normrank transformation was more powerful than Pearson’s and Spearman’s procedures when the distributions have less than normal kurtosis (platykurtic), when the distributions have greater than normal kurtosis (leptokurtic), and when the distribution is skewed. This is examined for testing if there is an …

Quantitative Verification For Massive Linear Systems, Qing Liu

School of Computing: Dissertations, Theses, and Student Research

The verification of linear systems has been an active area of research for decades. Reachability analysis is a key component in verification problems. It involves computing the system’s reachable set, the set of reachable states in the state space from a given set of initial states. Most verification methods primarily focus on qualitative verification, which answers whether or not a system may violate specified safety conditions. This paper extends this qualitative verification to quantitative verification by introducing a novel approach, employing probabilistic stars (Probstars) to compute reachable sets, which augment traditional star sets by integrating Gaussian-distributed random variables with …

Game-Theoretic Approaches To Optimal Resource Allocation And Defense Strategies In Herbaceous Plants, Molly R. Creagar

Department of Mathematics: Dissertations, Theses, and Student Research

Empirical evidence suggests that the attractiveness of a plant to herbivores can be affected by the investment in defense by neighboring plants, as well as investment in defense by the focal plant. Thus, allocation to defense may not only be influenced by the frequency and intensity of herbivory but also by defense strategies employed by other plants in the environment. We incorporate a neighborhood defense effect by applying spatial evolutionary game theory to optimal resource allocation in plants where cooperators are plants investing in defense and defectors are plants that do not. We use a stochastic dynamic programming model, along …

Memory Network-Based Interpreter Of User Preferences In Content-Aware Recommender Systems, Nhu Thuat Tran, Hady W. Lauw

Research Collection School Of Computing and Information Systems

This article introduces a novel architecture for two objectives recommendation and interpretability in a unified model. We leverage textual content as a source of interpretability in content-aware recommender systems. The goal is to characterize user preferences with a set of human-understandable attributes, each is described by a single word, enabling comprehension of user interests behind item adoptions. This is achieved via a dedicated architecture, which is interpretable by design, involving two components for recommendation and interpretation. In particular, we seek an interpreter, which accepts holistic user’s representation from a recommender to output a set of activated attributes describing user preferences. …

Convolutional Neural Network-Based Gene Prediction Using Buffalograss As A Model System, Michael Morikone

Complex Biosystems Program: Dissertations and Student Research

The task of gene prediction has been largely stagnant in algorithmic improvements compared to when algorithms were first developed for predicting genes thirty years ago. Rather than iteratively improving the underlying algorithms in gene prediction tools by utilizing better performing models, most current approaches update existing tools through incorporating increasing amounts of extrinsic data to improve gene prediction performance. The traditional method of predicting genes is done using Hidden Markov Models (HMMs). These HMMs are constrained by having strict assumptions made about the independence of genes that do not always hold true. To address this, a Convolutional Neural Network (CNN) …

A Comparison Of Computational Perfusion Imaging Techniques, Shaharina Shoha

Masters Theses & Specialist Projects

Dynamic contrast agent magnetic resonance perfusion imaging plays a vital role in various medical applications, including tumor grading, distinguishing between tumor types, guiding procedures, and evaluating treatment efficacy. Extracting essential biological parameters, such as cerebral blood flow (CBF), cerebral blood volume (CBV), and mean transit time (MTT), from acquired imaging data is crucial for making critical treatment decisions. However, the accuracy of these parameters can be compromised by the inherent noise and artifacts present in the source images.

This thesis focuses on addressing the challenges associated with parameter estimation in dynamic contrast agent magnetic resonance perfusion imaging. Specifically, we aim …

A Robust Model Reduction For The Optimal Boundary Feedback Stabilization Of Magnetizable Piezoelectric Beams, Md Rafi As Sadeq Ibn Emran

Masters Theses & Specialist Projects

The one-dimensional Partial Differential Equation (PDE) model of the wave equation, which describes wave dynamics of a wide-range of controlled mechanical systems, with a state feedback controller at its boundary is known to have exponentially stable solutions. Moreover, it is also reported that the several model reductions of the wave equation by the standard Finite Differences and Finite Elements approximations suffer from the lack of exponential stability (and exact observability without a state feedback controller) uniformly as the discretization parameter tends to zero. This is due to the loss of a uniform gap among the high-frequency eigenvalues as the discretization …

Modeling Biphasic, Non-Sigmoidal Dose-Response Relationships: Comparison Of Brain- Cousens And Cedergreen Models For A Biochemical Dataset, Venkat D. Abbaraju, Tamaraty L. Robinson, Brian P. Weiser

Rowan-Virtua School of Osteopathic Medicine Departmental Research

Biphasic, non-sigmoidal dose-response relationships are frequently observed in biochemistry and pharmacology, but they are not always analyzed with appropriate statistical methods. Here, we examine curve fitting methods for “hormetic” dose-response relationships where low and high doses of an effector produce opposite responses. We provide the full dataset used for modeling, and we provide the code for analyzing the dataset in SAS using two established mathematical models of hormesis, the Brain-Cousens model and the Cedergreen model. We show how to obtain and interpret curve parameters such as the ED50 that arise from modeling, and we discuss how curve parameters might change …

Using Medicare Claims To Estimate Risk-Adjusted Performance Of Pennsylvania Trauma Centers, Alexis M Zebrowski, Phillipe Loher, David G Buckler, Isidore Rigoutsos, Brendan G Carr, Douglas J Wiebe

Computational Medicine Center Faculty Papers

Trauma centers use registry data to benchmark performance using a standardized risk adjustment model. Our objective was to utilize national claims to develop a risk adjustment model applicable across all hospitals, regardless of designation or registry participation. Patients from 2013-14 Pennsylvania Trauma Outcomes Study (PTOS) registry data were probabilistically matched to Medicare claims using demographic and injury characteristics. Pairwise comparisons established facility linkages and matching was then repeated within facilities to link records. Registry models were estimated using GLM and compared with five claims-based LASSO models: demographics, clinical characteristics, diagnosis codes, procedures codes, and combined demographics/clinical characteristics. Area under the …

Mathematical Modeling Of Egain Droplets Sliding Down An Inclined Plane, Shawn Koohy, Kathryn Massey, Luis Schneegans, Megan Vezzetti, Keith Hillaire, Souradip Chattopadhyay, Jessie Chen, Carmen Lee, Karen Daniels

Undergraduate Research Symposium

Eutectic Gallium-Indium (EGaIn) is a room-temperature liquid metal alloy that dramatically changes its surface tension and dynamics under an applied electric field. EGaIn has been used heavily in soft electronics engineering due to its high conductivity, malleability, and safety. However, the absence of mathematical modeling in the current literature makes its behavior difficult to understand and predict. In this study, we present a one-dimensional lubrication model for the dynamics of an EGaIn droplet moving along an inclined plane. Our model incorporates essential physical effects and parameters including oxidation, capillary action, diffusion, gravity, and Marangoni effects. In particular, we incorporate effects …

Analysis Of An Seir Model With Non-Constant Population, Kylar Byrd, Tess Tracy, Sunil Giri, Swarup Ghosh

Student Research

Analysis of an SEIR model with Non-Constant Population
by Kylar Byrd and Tess Tracy, with Dr. Sunil Giri and Dr. Swarup Ghosh.

Mathematical modeling can be useful in helping us to understand disease dynamics. Epidemiological models consist of differential equations with variables and parameters defined to portray these dynamics. We will be presenting the mathematics involved in formulating and analyzing a model for a disease such as influenza. We will first explain a simple SIR model, and then we will introduce our model. We will be looking at an SEIR model that incorporates the use of an exposed class as …

Graphsearchnet: Enhancing Gnns Via Capturing Global Dependencies For Semantic Code Search, Shangqing Liu, Xiaofei Xie, Jjingkai Siow, Lei Ma, Guozhu Meng, Yang Liu

Research Collection School Of Computing and Information Systems

Code search aims to retrieve accurate code snippets based on a natural language query to improve software productivity and quality. With the massive amount of available programs such as (on GitHub or Stack Overflow), identifying and localizing the precise code is critical for the software developers. In addition, Deep learning has recently been widely applied to different code-related scenarios, ., vulnerability detection, source code summarization. However, automated deep code search is still challenging since it requires a high-level semantic mapping between code and natural language queries. Most existing deep learning-based approaches for code search rely on the sequential text ., …

Chatgpt As Metamorphosis Designer For The Future Of Artificial Intelligence (Ai): A Conceptual Investigation, Amarjit Kumar Singh (Library Assistant), Dr. Pankaj Mathur (Deputy Librarian)

Library Philosophy and Practice (e-journal)

Abstract

Purpose: The purpose of this research paper is to explore ChatGPT’s potential as an innovative designer tool for the future development of artificial intelligence. Specifically, this conceptual investigation aims to analyze ChatGPT’s capabilities as a tool for designing and developing near about human intelligent systems for futuristic used and developed in the field of Artificial Intelligence (AI). Also with the helps of this paper, researchers are analyzed the strengths and weaknesses of ChatGPT as a tool, and identify possible areas for improvement in its development and implementation. This investigation focused on the various features and functions of ChatGPT that …

Dynamic Function Learning Through Control Of Ensemble Systems, Wei Zhang, Vignesh Narayanan, Jr-Shin Li

Publications

Learning tasks involving function approximation are preva- lent in numerous domains of science and engineering. The underlying idea is to design a learning algorithm that gener- ates a sequence of functions converging to the desired target function with arbitrary accuracy by using the available data samples. In this paper, we present a novel interpretation of iterative function learning through the lens of ensemble dy- namical systems, with an emphasis on establishing the equiv- alence between convergence of function learning algorithms and asymptotic behavior of ensemble systems. In particular, given a set of observation data in a function learning task, we …

Response Of Planetary Waves And Tides To The 2019 Southern Hemisphere Ssw And Q2dw Enhancement In Jan-Feb 2020 Observed By Condor Meteor Radar In Chile And Adelaide Meteor Radar In Australia, Alan Liu, Zishun Qiao, Iain Reid, Javier Fuentes, Chris Adami

Publications

A new multi-static meteor radar (CONDOR) has recently been installed in northern Chile. This CONDOR meteor radar (30.3°S, 70.7°W) and the Adelaide meteor radar (35°S, 138°E) have provided longitudinally spaced observations of the mean winds, tides and planetary waves of the PW-tides interaction cases we present here. We have observed a Quasi-6-Day Wave (Q6DW) enhancement in MLT winds at the middle latitudes (30.3°S, 35°S) during the unusual minor South Hemisphere SSW 2019 by the ground-based meteor radars. Tidal analysis also indicates modulation of the Q6DW w/ amplitude ~15 [m/s] and diurnal tides w/ amplitude ~60 [m/s]. Another case we present …

Approximation By Basis Pursuit: Background And Application To The Construction Of Efficient Spline Approximations, Babita Timalsina

Graduate Student Scholarship

Basis Pursuit was developed primarily as a tool in the field of signal processing, beginning in the mid 1990’s. The idea is to model the behavior of discrete signals using a wide range of functional behaviors and scales and to obtain an accurate and efficient representation of the signal using a minimal number of functions from a large “dictionary” of possible behaviors. The key observation is by formulating the representation as an ℓ1 optimization, the problem can be posed as a linear program so that the optimal solution uses no more than the number of constraints - it must be …