Numerical Analysis and Computation Commons^™

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 …

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 …

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 …

Numalyze: Numerical Analysis Web Application, Dev Kapupara

Electronic Theses, Projects, and Dissertations

Numalyze is an online platform that allows users to run and apply different numerical methods in real time. The application is built using Python and the Flask web framework. It provides an interface where users input mathematical functions and parameters to see the results for root-finding and integration methods, and to also perform reductions on matrices. By using a light-weight web framework and self-coded algorithms which removes dependency on massive external libraries—this application connects theoretical concepts to their practical implementation. It enables students and researchers to visualize the series of steps that each algorithm takes to compute results. Moreover, the …

Robust And Efficient Solvers For Physics-Based Pde’S, Elizabeth Hawkins

All Dissertations

This work was partially supported by the U.S. Department of Energy under award DE- SC0025292, by NSF grant DMS 2152623, and by NSF grant DMS 2011490.

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Mathematical Multifaceted Integrated Capability Centers (MMICCs) program, under Field Work Proposal 22-025291 (Multifaceted Math- ematics for Predictive Digital Twins (M2dt)), Field Work Proposal 23-020467, and Computing and Information Sciences (CIS) investment area in the Laboratory Directed Research and Development program at Sandia National Laboratories. This written work is authored by an employee …

Domain Decomposition For Coupled Systems Of Fluid-Structure Interaction And Numerical Modeling For Thin Film Polymers, Amy De Castro

All Dissertations

We consider two primary areas of physical application in this work: fluid interaction systems with either linear elastic structures or with poroelastic structures, and thin film polymers, where the majority of the work focuses on the fluid-structure interaction systems.

In the first chapter, we present a strongly coupled partitioned method for fluid structure interaction (FSI) problems based on a monolithic formulation of the system which employs a Lagrange multiplier (LM). We prove that both the semi-discrete and fully discrete formulations are well-posed. To derive the partitioned scheme, a Schur complement equation, which implicitly expresses the Lagrange multiplier and the fluid …

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 …

Developing Predictive Mathematical Model For Optimizing Coating Weight Variation In Galvalume Production: A Case Study Of A Metal Industry, Victoria Mahabi

Tanzania Journal of Engineering and Technology (TJET)

Variations in coating weight for galvanized steel sheets can result in notable differences between batches. Such variations may cause various issues, such as diminished corrosion resistance, lower mechanical strength, and visual defects, which can ultimately drive-up costs, lead to customer dissatisfaction, and pose safety risks. Even with attempts to manage elements like air knife pressure and line speed, coating weight inconsistencies remain challenging. The research focuses on developing a predictive mathematical model designed to optimize variations in coating weight during Galvalume production. The critical parameters influencing coating weight variation were identified and analysed using a systematic literature review, primary data …