Applied Mathematics Commons^™

Robot-Based 3d Printing, Aaron Hoffman

Williams Honors College, Honors Research Projects

Details of a large-format 3D printer created to print experimental materials, test multi-axis print techniques, and quickly print large objects. The printer consists of a 7-axis robotic arm and pellet extruder, which are controlled by a PC. Experimental materials such as recycled polymers or carbon-fiber reinforced materials can be easily tested with the pellet format of the extruder. The printer can perform different printing techniques and can be used to experiment with material properties when using these techniques with different polymers. The print surface is around 5 times larger than the average commercial 3D printer, and the robotic arm provides …

Determination Of Spore Viability In Concrete Across Several Factors Using Most Probable Number, Samuel Boyer

Williams Honors College, Honors Research Projects

To determine the lowest concentration of spore added to polyurethane-cement composite (PUCCO) particles that can still germinate after curing in concrete. This research project is a small addition to the larger research project being undertaken by Mirza Mohammed Rashiduzzaman for his Masters. The larger project involves the use of fungal spores added in concrete to act as a self-healing component when cracks form in the concrete structure over time. These spores are suspended in a protective oil and loaded into small, hardened sponge-like PUCCO cubes to act as growth points when water and air can reach the PUCCO in the …

Uniform Convergence Of Deep Neural Networks With Lipschitz Continuous Activation Functions And Variable Widths, Yuesheng Xu, Haizhang Zhang

Mathematics & Statistics Faculty Publications

We consider deep neural networks (DNNs) with a Lipschitz continuous activation function and with weight matrices of variable widths. We establish a uniform convergence analysis framework in which sufficient conditions on weight matrices and bias vectors together with the Lipschitz constant are provided to ensure uniform convergence of DNNs to a meaningful function as the number of their layers tends to infinity. In the framework, special results on uniform convergence of DNNs with a fixed width, bounded widths and unbounded widths are presented. In particular, as convolutional neural networks are special DNNs with weight matrices of increasing widths, we put …

Symmetry Analysis Of The Canonical Connection On Lie Groups:Co-Dimension Two Abelian Nilradical With Abelian And Non Abelian Complement, Nouf Alrubea Almutiben

Theses and Dissertations

We consider the symmetry algebra of the geodesic equations of the canonical
connection on a Lie groups. We mainly consider the solvable indecomposable four,
five and six-dimensional Lie algebras with co-dimension two abelian nilradical, that
have an abelian and not abelian complement. In this particular case, we have only
one algebra in dimension four namely; A4,12 , and three algebras in dimension five
namely; A5,33, A5,34, and A5,35 In dimension six, based on the list of Lie algebras in
Turkowski’s list, there are nineteen such algebras namely; A6,1- A6,19 that have an
abelian complement, and there are eight algebras that …

Data Driven And Machine Learning Based Modeling And Predictive Control Of Combustion At Reactivity Controlled Compression Ignition Engines, Behrouz Khoshbakht Irdmousa

Dissertations, Master's Theses and Master's Reports

Reactivity Controlled Compression Ignition (RCCI) engines operates has capacity to provide higher thermal efficiency, lower particular matter (PM), and lower oxides of nitrogen (NOx) emissions compared to conventional diesel combustion (CDC) operation. Achieving these benefits is difficult since real-time optimal control of RCCI engines is challenging during transient operation. To overcome these challenges, data-driven machine learning based control-oriented models are developed in this study. These models are developed based on Linear Parameter-Varying (LPV) modeling approach and input-output based Kernelized Canonical Correlation Analysis (KCCA) approach. The developed dynamic models are used to predict combustion timing (CA50), indicated mean effective pressure (IMEP), …

Discontinuous Galerkin Methods For Compressible Miscible Displacements And Applications In Reservoir Simulation, Yue Kang

Dissertations, Master's Theses and Master's Reports

This dissertation contains research on discontinuous Galerkin (DG) methods applied to the system of compressible miscible displacements, which is widely adopted to model surfactant flooding in enhanced oil recovery (EOR) techniques. In most scenarios, DG methods can effectively simulate problems in miscible displacements.
However, if the problem setting is complex, the oscillations in the numerical results can be detrimental, with severe overshoots leading to nonphysical numerical approximations. The first way to address this issue is to apply the bound-preserving
technique. Therefore, we adopt a bound-preserving Discontinuous Galerkin method
with a Second-order Implicit Pressure Explicit Concentration (SIPEC) time marching
method to …

New Method For Computing The Euclidean Condition Number With Rim-C, Cody Mccarthy

Dissertations, Master's Theses and Master's Reports

The condition number, being critical to solving linear systems, has many impor-
tant applications. Specifically for robust control analysis, the Euclidean norm has
widespread use over the 1-norm and ∞-norm such as determining a control system’s
stability to uncertainty [1]. Much work has been done with estimating the Euclidean
condition number, but current algorithms for computing said condition number, with
large matrices, tend to run slow as well as requiring a large amount of computa-
tional resources. This report seeks to provide a more time efficient algorithm that
utilizes MATLAB’s eigs, svds, and normest commands as well as the recently …

Estimating Modeling Parameters For Covid-19 Spread On Campus, Aviel S. Crigger

Honors Undergraduate Theses

Understanding the true burden of community transmission of communicable diseases like COVID-19 is crucial for effective public health response. Clinical cases, while important, only represent a fraction of the actual disease prevalence within a population. In this thesis, we investigate methods to estimate parameters that link clinical cases to the true disease prevalence using a modified compartmental model known as SICR (Susceptible, Infected, Cases, Recovered). We employ Bayesian inference and ensemble Markov chain Monte Carlo (MCMC) simulations to analyze clinical case data provided by the University of Central Florida Health Center from 2020 to 2022. Our goal is to estimate …

Mathematical Modeling Of Coupled Heat And Mass Transfer In Metal-Hydride Hydrogen Storage Systems, Muhammad Hasnain

College of Graduate Studies: Theses & Dissertations

As a promising clean energy carrier hydrogen has recently gained significant interest, but its efficient and safe storage is a major challenge. Compared to the gaseous state and liquid state, metal hydrides (MH) offer a potentially more effective storage approach for hydrogen. However, the main challenge in this approach is the low thermal conductivity of the MH bed that leads to low heat transfer and ultimately to higher charging and discharging times. The purpose of this work is to develop an in-house comprehensive heat and mass transfer model for hydrogen sorption in MH reactors to simulate the dynamic behavior of …

Reducing Generalization Error In Multiclass Classification Through Factorized Cross Entropy Loss, Oleksandr Horban

CMC Senior Theses

This paper introduces Factorized Cross Entropy Loss, a novel approach to multiclass classification which modifies the standard cross entropy loss by decomposing its weight matrix W into two smaller matrices, U and V, where UV is a low rank approximation of W. Factorized Cross Entropy Loss reduces generalization error from the conventional O( sqrt(k / n) ) to O( sqrt(r / n) ), where k is the number of classes, n is the sample size, and r is the reduced inner dimension of U and V.

Unveiling The Power Of Shor's Algorithm: Cryptography In A Post Quantum World, Dylan Phares

CMC Senior Theses

Shor's Algorithm is an extremely powerful tool, in utilizing this tool it is important to understand how it works and why it works. As well as the vast implications it could have for cryptography

Sparse Representation Learning For Temporal Networks, Maxwell Mcneil

Electronic Theses & Dissertations (2024 - present)

Temporal networks arise in many domains including activity of social network users, sensor network readings over time, and time course gene expression within the interaction network of a model organism. Data of this type contains a wealth of prior information such as the connectivity among nodes (e.g., a friendship graph), and prior knowledge of expected temporal patterns (e.g., periodicity). Modeling these temporal and network patterns jointly is essential for state-of-the-art performance in temporal network data analysis and mining. Sparse dictionary encoding is one modeling approach for such underlying patterns. However, most classical approaches consider only one dimension of the data …

Leveraging Redundancy As A Link Between Spreading Dynamics On And Of Networks, Felipe Xavier Costa

Electronic Theses & Dissertations (2024 - present)

A constant quest in network science has been in the development of methods to identify the most relevant components in a dynamical system solely via the interaction structure amongst its subsystems. This information allows the development of control and intervention strategies in biochemical signaling and epidemic spreading. We highlight the relevant components in heterogeneous dynamical system by their patterns of redundancy, which can connect how dynamics affect network topology and which pathways are necessary to spreading phenomena on networks. In order to measure the redundancies in a large class of empirical systems, we develop the backbone of directed networks methodology, …

A Comparative Analysis Of A Family Of Advanced Iterative Optimization Methods In Nonlinear Regression, Tanmoy Kumar Debnath

College of Graduate Studies: Theses & Dissertations

Classical statistical supervised learning optimization techniques like the Gauss-Newton Iterative Method (GNIM), Weighted Gauss-Newton Iterative Method (WGNIM), Reweighted Gauss-Newton Iterative Method (RGNIM), and Levenberg-Marquart (LM) algorithm extend the nonlinear least squares method. The WGNIM improves model fitting by controlling heteroscedasticity in the linear and nonlinear models. A comparative analysis of the GNIM, WGNIM, RGNIM, and LM methods for fitting nonlinear models is presented. A step-wise diagnosis for structural multicollinearity in the reweighted linearized model is investigated via the Variance Inflation Factor (VIF) to determine variance inflation in the sequence of estimators for the model parameters. Under restricted multicollinearity levels in …

Numerical Modeling Of Thermal Runaway In Lithium-Ion Batteries Using Decomposition Kinetics And Inter-Cell Contact Resistance, Shehzad Khan

College of Graduate Studies: Theses & Dissertations

Lithium-ion batteries (LIBs) are central in numerous high-demand applications due to their high energy density and prolonged cycle life. Despite these advantages, their susceptibility to thermal runaway (TR) poses a significant safety risk, with the potential for catastrophic failures. This study focuses on the thermal behavior of prismatic lithium-ion cells, using a finite volume-based partial differential equation (PDE) solver developed in MATLAB and JULIA to model TR behavior. This solver accurately simulates transient behaviors, convection, diffusion, and source terms across various coordinate systems. By engaging in a series of increasing complex case studies, this research aims to identify the critical …

A Recursive Framework For Evaluating Moments Using Zero-Suppressed Binary Decision Diagrams, Brian Godwin Lim, Renzo Roel P. Tan, Jun Kawahara, Shin Ichi Minato, Kazushi Ikeda

Quantitative Methods and Information Technology Faculty Publications

The zero-suppressed binary decision diagram (ZDD) is a compact data structure widely used for the efficient representation of families of sparse subsets. Its inherent recursive structure also facilitates easy diagram manipulation and family operations. Practical applications generally fall under discrete optimization, such as combinatorial problems and graph theory. Given its utility, summarizing the subsets represented in the diagram using key metrics is of great value as this provides valuable insights into the characteristics of the family. The paper proposes a recursive algorithm to extract information on moments from families represented as a ZDD. Given a value for every element in …

Automatic Hemorrhage Segmentation In Brain Ct Scans Using Curriculum-Based Semi-Supervised Learning, Solayman H. Emon, Tzu-Liang (Bill) Tseng, Michael Pokojovy, Peter Mccaffrey, Scott Moen, Md Fashiar Rahman

Mathematics & Statistics Faculty Publications

One of the major neuropathological consequences of traumatic brain injury (TBI) is intracranial hemorrhage (ICH), which requires swift diagnosis to avert perilous outcomes. We present a new automatic hemorrhage segmentation technique via curriculum-based semi-supervised learning. It employs a pre-trained lightweight encoder-decoder framework (MobileNetV2) on labeled and unlabeled data. The model integrates consistency regularization for improved generalization, offering steady predictions from original and augmented versions of unlabeled data. The training procedure employs curriculum learning to progressively train the model at diverse complexity levels. We utilize the PhysioNet dataset to train and evaluate the proposed approach. The performance results surpass those of …

Addressing Spectral Bias Of Deep Neural Networks By Multi-Grade Deep Learning, Ronglong Fang, Yuesheng Xu

Mathematics & Statistics Faculty Publications

Deep neural networks (DNNs) have showcased their remarkable precision in approximating smooth functions. However, they suffer from the spectral bias, wherein DNNs typically exhibit a tendency to prioritize the learning of lower-frequency components of a function, struggling to effectively capture its high-frequency features. This paper is to address this issue. Notice that a function having only low frequency components may be well-represented by a shallow neural network (SNN), a network having only a few layers. By observing that composition of low frequency functions can effectively approximate a high-frequency function, we propose to learn a function containing high-frequency components by composing …

Characterizing Probabilities Of Outbreaks Of Dengue In Central Argentina Using A Temperature-Dependent Stochastic Model, Morgan H. Jackson, Elizabet L. Estallo, Cheng Ly, Michael A. Robert

Graduate Research Posters

Dengue virus (DENV) causes over 390 million infections and around 40,000 deaths worldwide each year. DENV is primarily transmitted by the mosquito Aedes aegypti, and both the life cycle of these mosquitoes and dengue transmission are significantly impacted by temperature. In the temperate region of Central Argentina, where dengue outbreaks first began in 2009, outbreaks of dengue can only occur due to new introductions of DENV from other regions. Due to the relationships between temperature and dengue, the risk of outbreak changes throughout the year.

We develop a stochastic model including temperature-dependent mosquito life history traits and transmission-related parameters. …

Optimizing Sports Outcome Prediction Through Feature Engineering And Machine Learning, Vitor S. Freitas

Graduate Theses/Dissertations

The challenge of predicting the outcome of a team game lies in the high complexity and dynamics of the sports data. This thesis focuses on the aspect of using feature engineering and the genetic algorithm to predict the winner and the score of various sports events. Generally, it deals with how machine learning algorithms are combined with state-of-the-art feature engineering techniques in sports datasets derived from various sports disciplines. In this thesis, five different machine learning models have been applied, classification and regression trees (CART), random forest (RF), stochastic gradient boosting (SGB), eXtreme gradient boosting (XGBoost), and extreme learning machine …