Mathematics Commons^™

Stroke Clustering And Fitting In Vector Art, Khandokar Shakib

Senior Independent Study Theses

Vectorization of art involves turning free-hand drawings into vector graphics that can be further scaled and manipulated. In this paper, we explore the concept of vectorization of line drawings and study multiple approaches that attempt to achieve this in the most accurate way possible. We utilize a software called StrokeStrip to discuss the different mathematics behind the parameterization and fitting involved in the drawings.

Mathematical Model For Giraffe Population Dynamics, Huntir Bass

Electronic Theses and Dissertations, 2020-2023

Since the 1980s the overall giraffe population has dropped at least 40% causing some researchers to label this rapid decline as the "Silent Extinction." Due to this plummet, understanding the behaviors of the giraffe population is absolutely necessary before they are on the brink of extinction. Through the usage of mathematical modeling methodologies, a general model is created to illustrate the relationship between juvenile and adult female giraffes through numerous interaction parameters. Variations on specific variables generate different simulations, which allows more biological accuracy. With each variation having an established coexistence equilibrium between the juvenile and adult female populations, the …

Various Dynamical Regimes, And Transitions From Homogeneous To Inhomogeneous Steady States In Nonlinear Systems With Delays And Diverse Couplings, Ryan Roopnarain

Electronic Theses and Dissertations, 2020-2023

This dissertation focuses on the effects of distributed delays modeled by 'weak generic kernels' on the collective behavior of coupled nonlinear systems. These distributed delays are introduced into several well-known periodic oscillators such as coupled Landau-Stuart and Van der Pol systems, as well as coupled chaotic Van der Pol-Rayleigh and Sprott systems, for a variety of couplings including diffusive, cyclic, or dynamic ones. The resulting system is then closed via the 'linear chain trick' and the linear stability analysis of the system and conditions for Hopf bifurcations that initiate oscillations are investigated. A variety of dynamical regimes and transitions between …

Actuarial Credibility Approach In Adjusting Initial Cost Estimates Of Transport Infrastructure Projects, Bartłomiej Rokicki, Krzysztof Ostaszewski

Faculty Publications – Mathematics

This paper presents a novel methodology based on the modified actuarial credibility approach. It allows for the adjustment of initial cost estimates of public infrastructure projects by accounting for the additional risk/uncertainty factor. Hence, it offers an interesting alternative to other existing forecasting methods. We test our approach by applying data for over 300 major infrastructure projects implemented in Poland between 2004 and 2020. We prove that, despite its simplicity, the actuarial credibility approach can deliver accurate cost estimates compared to more complex methods such as regression analysis (OLS) or machine learning (LASSO). In particular, we show that, although the …

The Role Of Interactive Features Within A Mathematics Storybook In Interpreting A Conflict And Conflict Resolution: The Case Of Three Fifth Graders, Mahtob Aqazade

Faculty Publications – Mathematics

Students often experience cognitive conflicts when trying to interpret negative numbers’ order and values because they do not correspond to their prior whole number knowledge. One way to trigger students’ cognitive conflicts and support their conflict resolution meaningfully is through stories. Thus, I used a temperature-related mathematics storybook—Temperature Turmoil—to highlight the cognitive conflict students often experience because of relying on the integers’ absolute value and introduce conflict resolution (i.e., integers have both absolute value and directed value). By incorporating interactive features, I used a multiple-case approach to describe three fifth graders’ cognitive conflict and conflict resolution experiences. Harry, Lola, and …

Analyzing Marriage Statistics As Recorded In The Journal Of The American Statistical Association From 1889 To 2012, Annalee Soohoo

CMC Senior Theses

The United States has been tracking American marriage statistics since its founding. According to the United States Census Bureau, “marital status and marital history data help federal agencies understand marriage trends, forecast future needs of programs that have spousal benefits, and measure the effects of policies and programs that focus on the well-being of families, including tax policies and financial assistance programs.”[1] With such a wide scope of applications, it is understandable why marriage statistics are so highly studied and well-documented.

This thesis will analyze American marriage patterns over the past 100 years as documented in the Journal of …

Energy As A Limiting Factor In Neuronal Seizure Control: A Mathematical Model, Sophia E. Epstein

CMC Senior Theses

The majority of seizures are self-limiting. Within a few minutes, the observed neuronal synchrony and deviant dynamics of a tonic-clonic or generalized seizure often terminate. However, a small epilesia partialis continua can occur for years. The mechanisms that regulate subcortical activity of neuronal firing and seizure control are poorly understood. Published studies, however, through PET scans, ketogenic treatments, and in vivo mouse experiments, observe hypermetabolism followed by metabolic suppression. These observations indicate that energy can play a key role in mediating seizure dynamics. In this research, I seek to explore this hypothesis and propose a mathematical framework to model how …

Mary Eleanor Spear's Importance To The History Of Statistical Visualization, Melanie Williams

CMC Senior Theses

This paper will demonstrate why Mary Eleanor Spear (1897-1986) is an important figure in the history of statistical visualization. She lead an impressive career working in the federal government as a data analyst before "data analyst" became a thing. She wrote and illustrated two comprehensive textbooks which furthered the art of statistical visualization. Her textbooks cover extensive graphing knowledge still valuable to statisticians and viewers today. Most notable of her works is her development of the box plot. In addition to Spear's career and contributions, this paper will also address the lack of female representation in science, technology, engineering, and …

Review Of Copula For Bivariate Distributions Of Zero-Inflated Count Time Series Data, Dimuthu Fernando, Mohammed Alqawba, Manar Samad, Norou Diawara

Mathematics & Statistics Faculty Publications

The class of bivariate integer-valued time series models, described via copula theory, is gaining popularity in the literature because of applications in health sciences, engineering, financial management and more. Each time series follows a Markov chain with the serial dependence captured using copula-based distribution functions from the Poisson and the zero-inflated Poisson margins. The copula theory is again used to capture the dependence between the two series.

However, the efficiency and adaptability of the copula are being challenged because of the discrete nature of data and also in the case of zero-inflation of count time series. Likelihood-based inference is used …

Recent Analytic Development Of The Dynamic Q-Tensor Theory For Nematic Liquid Crystals, Xiang Xu

Mathematics & Statistics Faculty Publications

Liquid crystals are a typical type of soft matter that are intermediate between conventional crystalline solids and isotropic fluids. The nematic phase is the simplest liquid crystal phase, and has been studied the most in the mathematical community. There are various continuum models to describe liquid crystals of nematic type, and Q-tensor theory is one among them. The aim of this paper is to give a brief review of recent PDE results regarding the Q-tensor theory in dynamic configurations.

Planning And Effects Of Equitable Teaching Practices In Emu Math 120 Class, Kyle Yapp

Senior Honors Theses and Projects

The purpose of this project is to evaluate the effects of implementing Equitable Teaching practices in Math 120 Calculus 1. We used the EQUIP instrument in order to measure the amount of participation from each student. We used the X-PIPS-M instrument in order to get the students' responses to the class as well as have Dr. Ross reflect as a teacher. We used the MCOPP+ in order for Dr. Ross to reflect as a teacher. We also used the Calculus 1 Concept Inventory assessment in order to evaluate students' content knowledge growth during the course. We found that students responded …

On The Chromatic Numbers Of Subgroup Lattices, Jacob C. Miles

Graduate Theses/Dissertations

In this thesis we investigate the chromatic number of the Hasse diagram of a subgroup lattice. We combine results of Bollobás and Tůma to show that there exist infnite groups whose subgroup lattices have arbitarily high chromatic numbers. We show that fnite supersolvable groups have bipartite subgroup lattices but that CLT and non-solvable groups may not have bipartite subgroup lattices. Lastly, we give a preliminary argument suggesting that there are an infnite number of non-solvable groups whose subgroup lattices are bipartite.

Several Problems In Nonlinear Schrödinger Equations, Tim Van Hoose

Masters Theses

“We study several different problems related to nonlinear Schrödinger equations….

We prove several new results for the first equation: a modified scattering result for both an averaged version of the equation and the full equation, as well as a set of Strichartz estimates and a blowup result for the 3d cubic problem.

We also present an exposition of the classical work of Bourgain on invariant measures for the second equation in the mass-subcritical regime”--Abstract, page iv.

Beyond Quenching Profile For Singular Semilinear Parabolic Partial Differential Equations With Mixed Boundary Conditions, Benjamin Thaitavorn

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Numerical Approximation To Ruin Probability Of Generalization Of Classical Risk Model, Kittiwat Woragate

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Random Forest Of Mixed Decision Trees And Minority Condensation Decision Trees For Class Imbalanced Problem, Suvaporn Homjandee

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

3d Building Internal Structural Component Segmentation From Point Cloud Data Using Dbscan And Modified Ransac With Normal Deviation Conditions, Thanapon Doougphummet

Chulalongkorn University Theses and Dissertations (Chula ETD)

Nowadays, the laser scanner plays an important role as a tool to capture building structure in a form of point cloud which can be used to draw a blueprint or a floor plan for reconstruction or renovation of an existing building. The point cloud data represent a shape or an object in three dimensions. This point cloud together with the utilization of Building Information Modeling (BIM) which is a workflow that provides information about the foundation and structure measurement of a building, make a planning and design to construction more convenient and efficient in several aspects than the traditional way. …

Connected Size Ramsey Numbers Of Matching And Some Graphs, Jirawat Mungtumklang

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Valuation Of American Commodity Options, Piyapoom Nonsoong

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this dissertation, we present analytical option pricing formulas for European and American options in which the price dynamics of a risky asset follows a meanreverting process with time-dependent parameter. The process can be adapted to describe both nonseasonal and seasonal variation in price, especially, in commodity markets such as agricultural commodities. The formulas are derived based on the solutions of partial differential equations showing that the values of both European and American options can be decomposed into two parts: the payoff of the option at initial time and the time-integral over the lifetime of the option, which is driven …

Random Forest Algorithm Using Quartile-Patternbootstrapping For Class Imbalanced Problem, Worawit Jitpakdeebodin

Chulalongkorn University Theses and Dissertations (Chula ETD)

Nowadays, classification in machine learning serves as a valuable tool for extracting and analyzing real-world datasets. However, an important issue in classification is the problem of class imbalance, which significantly impacts the performance of classifiers. In 2019, a novel approach for a decision tree induction was introduced to address This problem—the Minority Condensation Entropy (MCE) measure that can effectively handle imbalanced datasets. Subsequently, in 2021, a new outlier factor called the Mass ratio - variance Outlier Factor (MOF) was presented that can rank instances based on the dataset density. This thesis proposes a random forest algorithm using quartile-pattern Bootstrapping that …