Numerical Analysis and Computation Commons^™

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 …

Algebraic Multigrid Methods For Nonsymmetric And Indefinite Problems: Theory And Applications, Ahsan Ali

Mathematics & Statistics ETDs

Algebraic multigrid (AMG) is a well-established and highly efficient solver for symmetric positive definite (SPD) systems arising from elliptic and parabolic PDEs, while nonsymmetric systems from hyperbolic PDEs remain a significant challenge. This dissertation develops AMG methods and theory for nonsymmetric problems. First, we develop a novel approach combining mode constraints from energy-minimization AMG with local approximations of ideal restriction in $\ell$AIR, resulting in constrained $\ell$AIR (C$\ell$AIR), which demonstrates scalable convergence across advective and diffusive problems. Second, we extend optimal AMG theory by deriving spectral radius estimates for the two-grid error transfer operator using matrix-induced orthogonality, enabling convergence predictions for …

Derivation Of Adjoint Based Error Estimates For Nonlinear Ordinary Differential Equations With Application To Multistage Sir Models With Demographics, Daniel Alcala

Mathematics & Statistics ETDs

Ordinary Differential Equations (ODEs) are central to the mathematical modeling of various real-world phenomena, from mechanical systems governed by Newton’s laws to epidemic dynamics described by SIR-type ODEs. Since many ODEs do not admit closed-form analytic solutions, we approximate them numerically (e.g., with Euler’s, Runge–Kutta, or other such methods). This raises the key question: How accurate are these numerical solutions? In particular, reliably estimating the error in some quantity of interest (QoI) at time T without having an exact solution is of great scientific interest.

The first main contribution of this thesis is the development and analysis of adjoint-based error …

Gain Threshold Optimization Using Fano Resonance, Alina Oktiabrskaia

LSU Doctoral Dissertations

The study of resonances in electromagnetics plays a critical role in the design of optical systems. This dissertation investigates the interaction between resonance and gain in optical structures to establish a universal principle for achieving ultra-low-threshold lasing. Through the analysis of geometric symmetries, material properties, and coupling mechanisms, this research develops prototype structures applicable to a wide range of optical and electromagnetic systems. A range of models is considered, starting from a simple onedimensional string-resonator system (based on the model of H. Lamb), then advancing to two- and three-dimensional waveguide models, and culminating with a realistic high-contrast model in open …

Modeling, Analysis, And Prediction Of Covid-19 Dynamics With Interacting Subpopulations And Implicit Behavior Using Physics-Informed Neural Networks, Naima Aubry-Romero, Alonso Ogueda-Oliva, Padmanabhan Seshaiyer

Spora: A Journal of Biomathematics

In this paper, we consider an extended SEIR compartmental model that incorporates young and old interacting subpopulations, allowing for cross-group transmission dynamics. Implicit behavioral changes are included to determine the influence of social behavior on coronavirus transmission dynamics. The basic reproduction number, the average number of secondary cases of infection produced by a single primary case, is derived for both the explicit and implicit model using the next-generation matrix method. We solve the associated differential equation systems and estimate useful parameters in the explicit model using physics-informed neural networks (PINNs). Our results point to how the PINNs approach offers an …

Towards Effective Academia-Industry Collaborations: The Case Of Higher Learning Institutions In Tanzania, Fatuma S. Ikuja

Tanzania Journal of Engineering and Technology (TJET)

Industries are the main consumers of products from higher learning institutions (HLIs); graduates for employment and research outputs for socio-economic development. Research outputs from HLIs are commercialized as services or products facilitated by academia-industry collaborations. The collaborations are expected to address mismatch between labour market needs and HLIs’ products, which has resulted in graduates’ employability challenges. Despite their importance, effective academia-industry collaborations remain challenging. This study explores the effectiveness of Academia-Industry collaborations established by HLIs in implementing the Higher Education Economic Transformation (HEET) project (2021-2026) in Tanzania. One of the project objectives is to build functional linkages between industry and …

Fuzzy-Ahp Based Decision Support System For The Selection Of Optimal Maintenance Strategy For Meter Gauge Railway Infrastructure: A Review, Hamisi J. Maulid

Tanzania Journal of Engineering and Technology (TJET)

There are many uncertainties and complexities associated with maintaining Meter Gauge Railway (MGR) infrastructure, which calls for a methodical approach to decision-making. The development and application of a fuzzy-AHP-based decision support system (DSS) to select the optimal maintenance strategy for the MGR are presented in this study. The review covers research from 2013 to 2023 and focusses on the use of Multi-Criteria Decision Making (MCDM) and Fuzzy Analytic Hierarchy Process (Fuzzy-AHP) techniques in railway infrastructure maintenance. To manage the inherent uncertainties and subjective judgements involved in maintenance decision-making, the Fuzzy-AHP methodology combines fuzzy logic with the Analytic Hierarchy Process (AHP). …

The Role Of Internal Factors On Vehicular Mobility, Aziz Mdimi

Tanzania Journal of Engineering and Technology (TJET)

Vehicle mobility internal factors are influenced by the performance state of the road surface quality, governor, engine, gear train, differential unit and mobility unit. Studies on vehicular mobility models exist for off-road external factors but absent on on-road internal factors. The on-road internal factors model describes the vehicular mobility performance as a function of internal factors. In the current undertaking, results are generated by the determination of mobility performance characteristics with the application of 2nd Order Ordinary Differential Equations and using Laplace operator with MATLAB Software simulation. The effect of road surface against the time taken varies accordingly. At a …

Review On Gas-To-Liquids Conversion Technology: Lessons From Case Studies And Potential Strategies For Implementation In Tanzania, Joseph H. Kihedu

Tanzania Journal of Engineering and Technology (TJET)

This review paper explores the transformative potential of Gas-to- Liquids (GTL) technology for harnessing Tanzania's vast natural gas resources. With significant discoveries of natural gas reserves totalling up to 57 Tcf in fields such as Songosongo, Mnazi Bay, Block 1, 2, 3 and 4. Tanzania is positioned to leverage GTL technology to convert these resources into high-value liquid fuels like gasoline, diesel and naphtha. Review of GTL process, its products and applications has been done. By analysing successful GTL projects globally and drawing lessons applicable to Tanzania, this paper provides strategic recommendations for policymakers and stakeholders to foster GTL development. …

Fuzzy Logic-Based Decision Support System For Adoption Of Industry 4.0 Predictive Maintenance By Manufacturing Industries, Fred E. Peter

Tanzania Journal of Engineering and Technology (TJET)

In the context of Industry 4.0, predictive maintenance enhances operational efficiency by optimizing processes, minimizing downtime, and improving cost-effectiveness. However, implementing predictive maintenance requires a systematic approach due to its complexity. This study collected expert input from 15 food and beverage manufacturing industries located in Dar es Salaam, Tanzania, using a purposive sampling technique. Six representatives were selected from each industry, and their opinions were analyzed using MATLAB 7.6 through a fuzzy logic inference system. The analysis focused on key factors influencing Industry 4.0 technology adoption for predictive maintenance, including adoption intention (strategic decision, equipment data, perceived benefit) and perceived …

Assessment Of Digital Solutions For Conformity Assessment Of Legally Controlled Measuring Instruments In Tanzania, Faraja Nyoni

Tanzania Journal of Engineering and Technology (TJET)

The advent of state-of-the-art digital technologies since 2011 has led to the digital transformation of legal metrology practices to ensure the trustworthiness of software-controlled measuring instruments globally. Despite the digital transformation in legal metrological practices, the conformity assessment of legally controlled measuring instruments is manually done (i.e., paper-based) in Tanzania. The paper-based conformity assessment of legally controlled measuring instruments is prone to error and lacks efficiency and effectiveness. This study aimed to assess digital solutions for improving conformity assessment through a comprehensive survey conducted across various regions in Tanzania, targeting a stratified sample of 51 respondents from organizations involved in …

Towards Future Sustainable Infrastructure: The Role Of Technical Audit In Tanzania’S Public Works, George C. Haule

Tanzania Journal of Engineering and Technology (TJET)

This study aimed to investigate the vital role and impact of technical audits in promoting sustainable infrastructure development in Tanzania. The role and effects of technical audits in long-term infrastructure development were studied using a mixed-methods approach with both quantitative and qualitative parts. Data were collected through analysis of technical audit documentation, a semi-structured questionnaire, and stakeholder interviews. The study revealed the various dimensions of infrastructure investment projects, including initiation and planning, design, procurement of contractors and consultants, contract management, environment, health, and safety. The technical audit findings reported weaknesses or non-performance issues in infrastructure planning at the national level …

Stability Analysis And Extension Of A Discrete-Time Dynamical System For Scaffolded Learning, Kris H. Green, Bernard Ricca

Northeast Journal of Complex Systems (NEJCS)

Van Geert and Steenbeek [16] proposed a coupled, delayed, discrete-time deterministic dynamical system to model scaffolded learning. We provide a detailed analysis of their model, whose global dynamics are complicated by the presence of intersecting lines of non-isolated, nonhyperbolic fixed points. We also interpret some of the trajectories in the system that have interesting dynamics in the context of the teacher-student interactions, and propose an extension to the model that simultaneously collapses the lines of fixed points to single, isolated points and is easily interpreted. These results provide the foundation for guiding the collection and integration of experimental data to …

The Evolution Of Global Gold And Copper Trade Networks, Oleksandr Hulianskyi

Northeast Journal of Complex Systems (NEJCS)

Gold and copper have emerged as two of the most vital commodities in global trade. Despite serving distinct purposes, their international trade networks reveal interconnected patterns, critical to understanding the dynamics of global economics. This paper studies these attributes and their evolution during the last 36 years for both metals and finds correlations between them. The first part of the research is focused on the sustainability of networks through efficiency and robustness indexes; the second part is dedicated to interconnectedness – the Louvain and Bayesian SBM algorithms, partition, and modularity instruments are used. Community detection algorithms provide valuable insights into …

Exploring The Potential Of Large Language Models (Llms) To Simulate Social Group Dynamics: A Case Study Using The Board Game "Secret Hitler", Kaj Hansteen Izora, Christof Teuscher

Northeast Journal of Complex Systems (NEJCS)

This study explores the capacity of large language model-powered agents to simulate human-like behavior in multi-agent social systems. Using Secret Hitler — a hidden-role board game centered on trust, deception, and strategic communication — we evaluate how LLM agents navigate dynamic group interactions. Our findings show that agents exhibit human-like behaviors, including strategic temporal adaptation, contextual reasoning, and complex social cognition such as theory of mind and implicit coordination. Notably, 85% of agent decisions factored in at least two other players’ mental states, highlighting their capacity for multi-agent mental state inference. However, they struggled with key aspects of human gameplay, …

Coarse-Graining Spiking Reservoirs: Reducing Reservoir Size While Preserving Critical Dynamics, Tucker X. Mastin, Christof Teuscher

Northeast Journal of Complex Systems (NEJCS)

We propose an extension of renormalization into the domain of spiking neural networks, thereby providing a novel framework for coarse-graining neural networks without disrupting their critical properties. The proposed coarse-graining technique merges neurons and synaptic connections based on a graph-theoretic distance derived from synaptic weight strength and is configured to effectively prune the reservoir size while preserving the scale-free spiking dynamics indicative of criticality. Criticality in spiking neural networks may provide information-theoretic advantages by optimizing information processing and sensitivity to input. Using time-series prediction benchmarks, we demonstrate that networks operating at criticality exhibit up to 32% higher prediction accuracy before …

Multi-Level Differentiable Moving Particles With Partition Of Unity, Jinjin He

Dartmouth College Master’s Theses

Representing implicit geometry with intricate features has long been a challenge. Recent advances in Implicit Neural Representations (INRs) have shown great promise in applications such as 3D reconstruction, inverse rendering, and dynamic surface evolution. These methods leverage neural networks to model complex shapes continuously, offering advantages in resolution and flexibility over traditional discrete representations. Despite their success, efficiently handling fine geometric details and evolving dynamic scenes remains an open problem.

We introduce a differentiable moving particle representation based on the multi-level partition of unity (MPU) to model dynamic implicit geometries efficiently. Our approach employs two types of particles—feature particles and …

Orchestrating Complexity: The Art Of Virtual Leadership In System Modelling, Vijay Kumar Sonawane, Bipllab Roy, Purnendu Bikash Acharjee, Indu Pv

Northeast Journal of Complex Systems (NEJCS)

This paper explores the dynamics of virtual leadership within global remote work environments, focusing on the application of complex system modelling to understand and enhance leadership efficacy. The application of computational modelling has been a regular feature in economics, science and technology fields, however its application in virtual leadership with linkage to sport leadership appears to be a novel concept. Adopting a multidisciplinary approach, this paper incorporates Game Theory as a conceptual framework to make the leadership model more relevant and applicable that can offer simpler understanding of complex play of leadership drivers. The model incorporates five key leadership dimensional …

Leveraging Usage Of Ai In Education: Knowledge, Attitude And Behavioral Analysis On Students, Bipllab Roy, Purnendu Bikash Acharjee, Rohit Kumar Sharma, Ruptaheen Kramsapi, Shruti P

Northeast Journal of Complex Systems (NEJCS)

The paper explores the possible advantages and drawbacks of artificial intelligence (AI) on sustainability, with an emphasis on using AI to positively achieve SDGs. The study finds a significant vacuum in the literature on the association between knowledge, attitudes, and behaviors towards the use of AI tools and techniques in education and demographic characteristics (sex, age, education level, area of study, and city of origin). The purpose of this research is to close this knowledge gap and advance our understanding of how these demographic factors affect the integration of AI in educational environments. The study specifically aims to comprehend how …

Property Testing Ai: An Efficient Frontier, Paul Sopher Lintilhac

Dartmouth College Ph.D Dissertations

In this dissertation, we take a step towards addressing the major problem of a lack of standardized and rigorous approaches to testing and evaluation of AI systems. Taking inspiration from both the fields of Property Testing and Property Based Testing (for programs), we develop a novel taxonomy of partially overlapping classes of properties of AI systems, including simple properties, compound properties, higher order properties, data relation properties, and architecture-utility properties. We argue that this taxonomy categorizes a diverse set of AI traits -- including accuracy, fairness, robustness, monotonicity, point-wise and global privacy properties, sensitivity, and more -- according to the …

Filling Gaps In Scientific Data Sets Using Physics Informed Neural Networks: A Case Study In Velocity Fields, Ellen Saunders

Master's Theses

Gaps in scientific data sets are a persistent issue for researchers in a variety of fields, and while nothing makes up for missing out on real data, well-simulated synthetic data can be a useful tool. In the world of image processing, machine learning techniques have become quite sophisticated at taking an image with a missing component and filling in that space with something believable. The aim of this thesis is to take machine learning techniques similar to what gets used in image processing and repurpose them to infill gaps in scientific data sets in a realistic manner. This thesis compares …

Stability Insights From Modeling Chronic Myelogenous Leukemia, Giovani Thai

Master's Theses

This thesis centers around a model for chronic myelogenous leukemia (CML) as it behaves under imatinib treatment, a common medication for CML patients, and the anti-leukemia immune response. The dynamics are represented with a system of nonlinear delay-differential equations first constructed by Kim et al. in 2008, capturing population changes of T-cells and various CML growth stages. We investigate stability in both the clinical and mathematical sense. Through numerical simulations, we computationally incorporate a supplementary treatment plan to determine its effectiveness in aiding immune response and medication in achieving remission and full elimination. The primary goal is to conduct a …

From Neural Networks To Large Language Models: Innovations In Financial Ai, Mathematical Reasoning, And Structured Data Representation, Junyi Ye

Dissertations

This dissertation explores the evolution and application of artificial intelligence techniques across three critical domains: financial modeling, mathematical reasoning, and structured data analysis. The dissertation presents seven research projects that chart a progression from specialized neural architectures to sophisticated large language models (LLMs), contributing novel methodologies and frameworks at each stage.

In the financial domain, the research first introduces TS-Mixer, a MLP-based architecture for time-series forecasting that captures both feature relationships and temporal dependencies through a simple yet effective design, outperforming more complex models in S&P500 index prediction. The dissertation then presents DySTAGE, a dynamic graph representation learning framework that …

Efficient Solvers And Anderson Acceleration For The Bingham Equations, Victoria L. Fisher

All Theses

This work studies two techniques utilized to solve the Bingham equations that model viscoplastic flow. An Uzawa-type iterative procedure is first analyzed and tested for poor convergence of velocity and stress. We apply Anderson acceleration (AA) to this method and show improved convergence rates for both velocity and stress. A solver utilizing regularization is introduced, and AA is also applied to display better convergence results. We propose a new method that combines these two solvers and applies Anderson acceleration.

Using Gaussian Process Regression To Learn Thermodynamic Equations Of State With Uncertainty Quantification, Austen T. Lee

Chemical Engineering Undergraduate Honors Theses

This study investigates the use of derivative-informed Gaussian Process (GP) models to estimate thermodynamic behavior across temperature and density by building a Helmholtz-based equation of state. Argon, a stable monatomic gas, was chosen as a case study within the vapor region. The GP model was trained using values of experimentally measurable properties found by taking first and second derivatives of the original potential function. Results show that while the GP model offered uncertainty quantification and informed thermodynamic behavior, it predicted values that deviated from the ground truth depending on the property. The model exhibited high confidence in regions with substantial …

Solution Of Preconditioned Nonsymmetric Saddle Point Systems Through Modified Conjugate Gradient Iteration, Samson Ayo

Dissertations

In this dissertation, we present an iterative method (Preconditioned Nonsymmetric Saddle Point Conjugate Gradient) for simultaneously solving forward ($A{\bf x}={\bf b}$) and adjoint ($A^T{\bf y}={\bf g}$) linear systems. Our approach involves constructing an augmented nonsymmetric saddle point matrix that has a real positive spectrum and developing a conjugate gradient-like iteration for this matrix. We investigate the use of Schur Complement preconditioners with block-diagonal factorization computed by an incomplete QR factorization of $A$ to speed up the convergence of our method and compare the results to the preconditioned generalized least squares residual (GLSQR) and quasi-minimal residual (QMR) methods. We develop quadrature …

Sliding Window Method For Simulating Action Potentials In Axons, Hayden Reed

Honors Theses

ABSTRACT Hodgkin and Huxley’s nonlinear partial differential equations model the excitation and propagation of action potentials in neurons, and there have been numerous attempts at finding the best numerical solution method. This thesis proposes a novel approach to solving these equations: the Sliding Window method, in which a fixed sub-interval is found through capturing the signal’s head and tail. The system is then solved on the sub-interval instead of the entire interval. Using the Sliding Window technique also involves implementing the backward and forward Euler methods and the finite difference method. It will be demonstrated that, in utilizing the Sliding …

A Spectroscopic Survey Of Atmospheres Of Super-Earths, Luke Brust

Honors Theses

Recent research has made it possible to use spectroscopy to analyze the composition of the atmospheres of exoplanets, planets that orbit other stars. Most projects thus far have focused on the atmospheres of gas giants, as it is less challenging to observe them with available equipment. This project studies the atmospheres of four Super- Earths, planets that have a mass greater than the Earth but smaller than Neptune. This is accomplished by processing the raw spectroscopic data from the Hubble Space Telescope and modeling the atmosphere using the program 𝝉-Rex3. This survey found clear results from two of the selected …

The Numerical Method For Finding All The Zeros Of A Function F (X) On An Interval [A,B], Franissa Simon

Honors Theses

In this study, we develop a simple mathematical method for finding all the roots of a function on a specified interval. Existing classical numerical methods, including the Bisection Method, Secant Method, and Newton Method, cannot find all the zeros of a function f (x) on an interval [a,b]. Popular numerical root solvers like Matlab’s ‘fzero’, Maple’s ‘fsolve’, and SageMath’s ‘find_root’ typically yield only a single zero. This thesis explores a proposed interval computation bisection method, a systematic approach based on the traditional Bisection Method and interval computation. Unlike traditional bisection, which relies on the intermediate value theorem, this approach uses …

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 …