Digital Commons Network^™

Univariate Extreme Value Analysis Of Quantitative Investment Management, George Agbenyega Zumanu

Graduate Research Theses & Dissertations

The evolution of product development within the variable annuity (VA) business have sparked interest in quantitative investment management, particularly as most VA issuers have integrated volatility-controlled funds into their annuity portfolios. Despite the existence of empirical research on statistical analysis of extreme values in conventional investments, there has been a notable gap in research focus towards risk modeling in volatility-controlled funds.

This study contributes by analyzing and modeling the extreme values of investments in volatility-controlled funds, comparing them to conventional equity funds. The financial returns of S&P Dow Jones Indices (SPDJI) indices - SPXTR, risk control SPXT18UT, and managed risk …

Explicit Proximal Gradient Methods: Bridging Theory And Practice In Optimization, Cassandra Mohr

Graduate Research Theses & Dissertations

Convex optimization problems are central to numerous fields, including machine learning, signal processing, and image reconstruction. The development and analysis of algorithms for solving splitting optimization problems constitutes a significant area of research. In particular, we investigate a proximal gradient splitting method (PGM) with an explicit linesearch for finding the solution of nonsmooth optimization problems, where the objective function is the sum of two convex functions.

We focus on cases where one of the functions is differentiable, without imposing any Lipschitz continuity assumption on its gradient. We establish the proper definition of the linesearch, and demonstrate that this version of …

Julia Limiting Directions Of Quasiregular Maps, Julie Marie Steranka

Graduate Research Theses & Dissertations

In this dissertation, we study the set of Julia limiting directions of quasiregular maps. The work combines the study of dynamics of quasiregular maps and applications of nonlinear potential theory to quasiregular maps. Our main result shows that the set of Julia limiting directions of a transcendental-type $K$-quasiregular map $f:\R^n\to \R^n$ must contain a component of a certain measure, depending on the dimension $n$, the maximal dilatation $K$, and the order of growth of $f$. In particular, we show that if the order of growth is small enough, then every direction is a Julia limiting direction. The main tool in …

Explicitly Counting Subspaces Of Given Height Defined Over A Field Of Rational Functions, Kakoli Bhuyan

Graduate Research Theses & Dissertations

A height function measures the complexity of mathematical objects, usually points on some projective variety. There are previous results that estimate the number of subspaces of bounded height defined over number fields and function fields over a finite field. These results are asymptotic estimates as the height bound tends to infinity. In this dissertation we derive an explicit counting of the number of subspaces of given height defined over a field of rational functions.

Farey Recursion And Hyperbolic Dehn Filling, Jose Ebenezer Martinez

Graduate Student Theses, Dissertations, & Professional Papers

In this work, we present a solution to William Thurston's edge gluing equations for Dehn fillings of hyperbolic 3-manifolds. This is done for triangulations that involve the layered solid torus. Our approach uses Farey recursive functions, and we present a Farey recursive function that provides a solution to the gluing equations for any hyperbolic Dehn filling admitting a triangulation by the layered solid torus. We provide examples that demonstrate our solution for multiple 3-manifolds, and study the roots of the corresponding Farey recursive polynomials. As an additional application of our solution, we provide a formula for the complex length of …

Snow Spheres And Ice Cubes, John Adam

Mathematics & Statistics Faculty Publications

This article, titled "Snow spheres and ice cubes," discusses the melting of snowballs and ice cubes. It explains that in standard calculus textbooks, it is shown that a snowball melting at a rate proportional to its surface area will have its radius decrease at a constant rate, assuming it remains spherical as it melts. The article then poses several questions related to this concept, including the proportion of a smaller snow sphere that remains when half of a larger one has melted, the value of p for which the smaller sphere first melts, and the volume reduction factor for cubes …

Preface, Mohamed Mahdi Tekitek, Manfred Krafczyk, Li-Shi Luo

Mathematics & Statistics Faculty Publications

[Introduction] Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications, a macroscopic or continuum description has usually been sufficient due to the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the macroscopic …

Optimizing Microbe-Infected Mosquito Release: A Stochastic Model For Malaria Prevention, Steeven Belvinos Affognon, Henri E.Z. Tonnang, Philip Ngare, Benard Kipchumba Kiplangat, Shirley Abelman, Jeremy K. Herren

All Peer-Reviewed Publications

Malaria remains a critical public health challenge in Africa, demanding innovative control strategies. This study introduces a novel approach using Microsporidia MB-infected mosquitoes and stochastic optimal control within a Lévy process framework to regulate mosquito release strategies. The primary goal is to optimize Microsporidia MB prevalence within mosquito populations to disrupt Plasmodium transmission to humans. By incorporating Lévy noise into the modeling process, we capture the inherent randomness of mosquito dynamics, improving intervention accuracy. The model, guided by the Hamilton–Jacobi–Bellman (HJB) equation, optimizes release protocols while accounting for key environmental factors like seasonality and temperature fluctuations. Results show that intervention …

Gwid: An R Package And Shiny Application For Genome-Wide Analysis Of Ibd Data, Soroush Mahmoudiandehkordi, Mehdi Maadooliat, Steven J. Schrodi

Mathematical and Statistical Science Faculty Research and Publications

Summary

Genome-wide identity by descent (gwid) is an R package developed for the analysis of identity-by-descent (IBD) data pertaining to dichotomous traits. This package offers a set of tools to assess differential IBD levels for the two states of a binary trait, yielding informative and meaningful results. Furthermore, it provides convenient functions to visualize the outcomes of these analyses, enhancing the interpretability and accessibility of the results. To assess the performance of the package, we conducted an evaluation using real genotype data derived from the SNPs to investigate rheumatoid arthritis susceptibility from the Marshfield Clinic Personalized Medicine Research Project.

Availability …

Extremal Graphs For Widom–Rowlinson Colorings In K-Chromatic Graphs, John Engbers, Aysel Erey

Mathematical and Statistical Science Faculty Research and Publications

The Widom–Rowlinson graph, H_WR , is the fully looped path on three vertices. Let hom(G,H_WR) be the number of graph homomorphisms from G to H_WR or, equivalently, the number of H_WR-colorings of G. We investigate extremal graphs for hom(G,H_WR) for G in the family of k-chromatic graphs subject to various connectivity requirements. In particular, we determine the graphs G maximizing hom(G,H_WR) in the families of n-vertex k-chromatic graphs, n-vertex connected k-chromatic graphs, n-vertex k-chromatic graphs with c components, n …

Multicolor Bipartite Ramsey Number Of Double Stars, Gregory M. Decamillis

Honors Undergraduate Theses

The core idea of Ramsey theory is that complete disorder is impossible. Given a large structure, no matter how complex it is, we can always find a smaller substructure that has some sort of order. For positive integers $n, m$, the double star $S(n,m)$ is the graph consisting of the disjoint union of two stars $K_{1,n}$ and $K_{1,m}$ together with an edge joining their centers. The $k$-color bipartite Ramsey number of $ S(n,m)$, denoted by $r_{bip}(S(n,m);k)$, is the smallest integer $N$ such that, in any $k$-coloring of the edges of the complete bipartite graph $K_{N,N}$, there is a monochromatic copy …

A Journey From Univariate To Multivariate Functional Time Series: A Comprehensive Review, Hossein Haghbin, Mehdi Maadooliat

Mathematical and Statistical Science Faculty Research and Publications

Functional time series (FTS) analysis has emerged as a potent framework for modeling and forecasting time-dependent data with functional attributes. In this comprehensive review, we navigate through the intricate landscape of FTS methodologies, meticulously surveying the core principles of univariate FTS and delving into the nuances of multivariate FTS. The journey commences with an exploration of the foundational aspects of univariate FTS analysis. We delve into representation, estimation, and modeling, spotlighting the effectiveness of various parametric and nonparametric models at our disposal. The stage then transitions to multivariate FTS analysis, where we confront the intricacies posed by high-dimensional data. We …

Conventions, Definitions, Identities, And Other Useful Formulae, Robert A. Mcnees Iv

Physics: Faculty Publications and Other Works

As the name suggests, these notes contain a summary of important conventions, definitions, identities, and various formulas that I often refer to. They may prove useful for researchers working in General Relativity, Supergravity, String Theory, Cosmology, and related areas.

Analysis Of Sir Model With Optimal Control Strategy For A Simple Traffic Congestion Process, Ratna Herdiana, Zani Anjani Rafsanjani, R. Heru Tjahjana, Yogi Ahmad Erlangga, Moch Fandi Ansori

All Works

Traffic analysis on highways at the macroscopic level is very similar to the analysis of the spread of infectious diseases, namely the susceptible-infected-recover (SIR) model. We propose the SIR model with a control variable. The dynamics with fixed control and stability of the model are analyzed. Sensitivity analysis was also carried out. Variable control is applied as an effort to regulate or change the duration of the green light at an intersection. We obtain an optimal control strategy when the control is time-dependent. Numerical results show the positive impacts of implementing the control to susceptible vehicles and treatment for congested …

Random Forests Regression For Soft Interval Data, Paul Gaona-Partida, Chih-Ching Yeh, Yan Sun, Adele Cutler

Mathematics and Statistics Faculty Publications

Analyzing soft interval data for uncertainty quantification has attracted much attention recently. Within this context, regression methods for interval data have been extensively studied. As most existing works focus on linear models, it is important to note that many problems in practice are nonlinear in nature and the development of nonlinear regression tools for interval data is crucial. This paper proposes an interval-valued random forests model that defines the splitting criterion of variance reduction based on an L₂ type metric in the space of compact intervals. The model simultaneously considers the centers and ranges of the interval data as …

Structure Identification For High-Dimensional Data In The Vicinity Of Bear Lake, Ben Shaw, Haley Burger, Brennan L. Bean, Kevin R. Moon

Mathematics and Statistics Faculty Publications

This report focuses on seven water quality measurements taken at 43 different depths on the Bear Lake, Utah-Idaho for the months of June - November in the years 2018 - 2023. These measurements create a high-dimensional dataset on which we apply state-of-the-art machine learning (ML) techniques to look for low-dimensional structure in the data. A similar effort was made for weather measurements taken near the lake. Our analysis reveals that water quality measurements tend to cluster (i.e., group together) by year, while weather measurements tend to cluster by time of the year. This in mind, we explore potential drivers of …

Perfect Codes On T-Cayley Graphs, Kantapong Wannatong

Chulalongkorn University Theses and Dissertations (Chula ETD)

Let G be a finite group with the identity e and t ∈ N. In this dissertation, we study perfect codes in a t-Cayley graph of G. Let H be a subgroup of G and k ∈ {1, . . . , t}. We have a necessary and sufficient condition for a collection Ω of subsets of G such that H × {1, . . . , k} is a perfect code in t-Cayley graph Cay(G× {1, . . . , t}, Ω). In addition, we obtain criterions for determining if H × {1, . . . , t} is …

Stochastic And Fuzzy Unit Commitment Models To Accommodate Solar Energy And Electric Vehicle Charging Penetration, Sukita Kaewpasuk

Chulalongkorn University Theses and Dissertations (Chula ETD)

This dissertation investigates the integration of renewable energy and electric vehicle (EV) consumption in the power system of Thailand. As the country moves towards sustainability, the production sector is experiencing a significant penetration of renewable energy sources, while the consumption sector is observing an increasing adoption of EVs. The unit commitment model is commonly used for electricity production planning to minimize costs and ensure system stability. However, the uncertainties associated with renewable energy output and EV charging consumption challenge the characteristic of the net load demand prediction. This study focuses on developing robust unit commitment models that consider the high …

Spatial Data Analysis For Household Income And Expenditure In Thailand, Jirayut Rattana

Chulalongkorn University Theses and Dissertations (Chula ETD)

Poverty has been a serious problem for many countries throughout the world, particularly during the COVID-19 pandemic. Due to the pandemic, many people lost their jobs and encountered economic. Therefore, the government and policy planners need an effective strategy to improve the country's economy. An essential component of these strategies involves analyzing socio-economic indicators, a field extensively explored by statisticians, economists, and policymakers. In Thailand, methodologies such as the World Bank method, Empirical Bayes, and Hierarchical Bayes have been applied to tackle poverty. However, these approaches often overlook the integration of spatial information in their analyses. In this study, we …

System Of Stochastic Grey Differential Equations With Singular Spectrum Analysis For Precious Metal Prices Forecasting, Rammarat Panadsako

Chulalongkorn University Theses and Dissertations (Chula ETD)

โลหะมีค่าเป็นกลุ่มโลหะที่มีมูลค่าทางเศรษฐกิจสูงกว่าโลหะทั่วไป ดังนั้นการพยากรณ์ราคาของโลหะมีค่าจึงเป็นหนึ่งปัญหาที่น่าสนใจ ซึ่งการพยากรณ์ราคาของโลหะมีค่ามีหลากหลายวิธี โดยวิทยานิพนธ์ฉบับนี้มีจุดประสงค์เพื่อพัฒนาระบบสมการเชิงอนุพันธ์เกรย์สโตแคสติกกับการวิเคราะห์สเปกตรัมเอกฐาน (SGDE+SSA) ในการพยากรณ์ราคาของทองคำ เงิน แพลทินัม และแพลเลเดียม ในขั้นตอนแรกจะทำการสร้างแบบจำลอง SGDE+SSA แบบหนึ่งมิติ เพื่อพยากรณ์ราคาของโลหะมีค่าทั้งสี่ชนิดโดยไม่พิจารณาค่าสหสัมพันธ์ของโลหะเหล่านี้ แต่ในความเป็นจริงราคาของโลหะเหล่านี้มีความสัมพันธ์กัน ดังนั้นแบบจำลอง SGDE+SSA แบบหลายมิติจึงถูกสร้างขึ้น โดยมีการพิจารณาค่าสหสัมพันธ์ที่เกิดจากการวิเคราะห์ข้อมูลราคาในอดีตเพื่อให้แบบจำลองมีความเหมาะสมกับสถานการณ์จริงมากยิ่งขึ้น สำหรับการวิเคราะห์ความอ่อนไหวจะศึกษาโดยการพัฒนาวิธีการคัดเลือกค่าพารามิเตอร์เพื่อเพิ่มประสิทธิภาพของแบบจำลอง นอกจากนี้ค่าคาดหวังและค่าความแปรปรวนของผลเฉลยทางตัวเลขถูกแสดงโดยคำนวณจากแบบจำลอง ความแม่นยำของแบบจำลอง SGDE+SSA แบบหนึ่งมิติ และแบบจำลอง SGDE+SSA แบบหลายมิติ จะถูกแสดงผ่านค่า MAPE ซึ่งเป็นการเปรียบเทียบระหว่างราคาจากแบบจำลองและราคาของโลหะมีค่าในอดีตตั้งแต่เดือนมกราคม พ.ศ. 2548 ถึง เดือนมกราคม พ.ศ. 2567 ผลการศึกษาครั้งนี้พบว่าแบบจำลอง SGDE+SSA แบบหนึ่งมิติสำหรับราคาการพยากรณ์ในช่วงชุดการเรียนรู้ และสำหรับสำหรับราคาที่พยากรณ์ในช่วงข้อมูลชุดทดสอบ แบบจำลอง SGDE+SSA แบบหนึ่งมิติมีความเชี่ยวชาญในการคาดการณ์ราคาของเงิน ในขณะที่แบบจำลอง SGDE+SSA แบบหลายมิติมีประสิทธิภาพในการทำนายราคาของทองคำและแพลทินัม โดยรวมแล้วแบบจำลองเหล่านี้มีประสิทธิภาพในการทำนายราคาทองคำ เงินและแพลทินัม

Homotopy Conjugate Of Continuous Map, Thitipon Phuksawad

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we introduce the concept of homotopy conjugate, which is weaker than topological conjugate, for continuous maps. We study the properties of a homotopy conjugate related to the fixed space, the orbit space, and the mapping cylinder. Moreover, we prove that affine maps on R™ with at least one fixed point are all homotopy conjugate.

Logistic Stochastic Differential Equation Driven By Fractional Brownian Motion, Thanayuth Promkong

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this work, the logistic stochastic differential equation (SDE) driven by fractional Brownian motion (FBM) is proposed. We derive the exact solution of this SDE using the fractional Itô's formula with respect to FBM and investigate the probabilistic properties of the solution, namely the mean and the $k$-th moment, using Taylor series approximation. The simulation of sample paths using the direct formula of the exact solution of this SDE driven by FBM with various Hurst parameters, along with that of the corresponding SDE driven by standard Brownian motion, is performed to demonstrate the behaviors of these SDEs and affirm our …

Pricing Option On Commodity Under Schwartz Model By Using Finite Difference Method, Peerawit Kalaphakdee

Chulalongkorn University Theses and Dissertations (Chula ETD)

This work aims for finding prices of options with underlying assets considered as commodities, where the price of commodity is assumed to follow a mean-reverting Ornstein-Uhlenbeck process, namely, the Schwartz one-factor model. The prices of both European and American options are obtained by employing the finite different methods (FDMs) for solving parabolic partial differential equations (PDEs) generated from Feynman-Kac theorem. In this work, we construct three FDMs to solve PDEs, namely FTCS, BTCS and CN methods. The accuracy of FDMs are validated and confirmed by numerical examples for European options by comparing with analytical results from Black-Scholes type formula and …

Fuzzy Digital Signature Scheme For Binary Noisy Strings With Respect To Hamming Distance, Ittanee Srikham

Chulalongkorn University Theses and Dissertations (Chula ETD)

One of the risks associated with public key infrastructure (PKI) pertains to the security of the user's private key. Given the imperative for stringent protection of this key, a proposed solution to mitigate this risk involves the utilization of biometric information. Although biometric information is fuzzy, it cannot be used directly as a cryptographic key. Thus, our investigation commenced into the exploration of ``Signature Scheme with a Fuzzy Private Key" by Takahashi et al. They introduced a new concept of digital signature called ``fuzzy signature" for real vectors with $L_{\infty}$ metric. A fuzzy signature is a signature scheme that uses …

Adjustment Of Ridge Estimator For Linear Regression Model With Multicollinearity, Sittinon Pumpuang

Chulalongkorn University Theses and Dissertations (Chula ETD)

Linear regression model is one of important statistical tools applied in many different problems. Therefore, several studies in developing tools for linear regression models have brought interests from statisticians. One such problem is to find an efficient method for parameter estimation. Several different methods have been proposed in literature such as the ordinary least square method which has been widely used in application. However, the least square estimator has high error when there exists a multicollinearity problem. This, statisticians have developed alternative parameter estimation methods for linear regression models with multicollinearity such as the ridge regression. In this thesis, we …

Fixed Point And Periodic Cycle Of Sequence Arises From Number Of Factors, Thanapong Jaitrakoon

Chulalongkorn University Theses and Dissertations (Chula ETD)

Let. {an} and {bn} be sequences of positive integers. For each positive integer n., define an+1 to be the eube of the number of positive factors of an and define bn+1 to be the forth power of the number of positive factors of bn. This thesis proves that (i) if a1 > 1, then (an) eventually becomes the fixed point, namely 21952 or 64000, or {an}eventually becomes a sequence having periodie cycle of prime period 2, namely (64, 343) or (343, 64); (ii) if b1 > 1, then {bn} is eventually the fixed point, namely 625, 6561 or 4100625.

Some Properties Of S-Multiplication Modules And S-Comultiplication Modules, Kanrop Hukaew

Chulalongkorn University Theses and Dissertations (Chula ETD)

Let R be an associative ring with identity, and all modules be unitary right R- modules. In 2020, D. D. Anderson et al. introduced the concept of S-multiplication modules, which is a generalization of multiplication modules. Two years later, E. Yildiz et al. introduced the dual notion of S-multiplication modules called S- comultiplication modules. Moreover, S-comultiplication modules are also a gen- eralization of comultiplication modules. In this thesis, we will explore several properties of both S-multiplication modules and S-comultiplication modules. We will provide examples of S-multiplication modules and S-comultiplication modules. Additionally, we demonstrate that the concepts of S-multiplication modules, sim- …

Prime Intersection Graphs Of Ideals Of Commutative Artinian Rings, Nuttawut Sangjaer

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we study prime intersection graphs of ideals of commutative Artinian rings. We work on the connectedness, completeness and planarity of the graphs and characterize the star graphs for these graphs. We calculate graph \linebreak parameters and find the radius and a center of the graphs. Moreover, we determine the degree of each vertex when the vertex set is finite, and characterize the Eulerian and Hamiltonian properties of the graphs.

Prediction Of Optimal Binding Constraints Of Linear Programming Problem Using Deep Learning, Natdanai Kafakthong

Chulalongkorn University Theses and Dissertations (Chula ETD)

This thesis presents innovative deep learning models designed to enhance the efficiency of solving linear programming, transportation, and traveling salesman problems. The first model, LP-Net, predicts the binding optimal constraints in linear programming problems, achieving faster solution times compared to traditional solvers like CPLEX. The second model, Transport-Net, predicts optimal basic feasible arcs for transportation problems, demonstrating significant speedups and superior scalability over both CPLEX and Gurobi in large-scale instances. The third model, TSP-Net, addresses the traveling salesman problem by predicting an initial near-optimal tour, outperforming Gurobi and genetic algorithms in computational efficiency. Collectively, these deep learning approaches offer transformative …

Facilitating Mathematics And Computer Science Connections: A Cross-Curricular Approach, Kimberly E. Beck, Jessica F. Shumway, Umar Shehzad, Jody Clarke-Midura, Mimi Recker

Publications

In the United States, school curricula are often created and taught with distinct boundaries between disciplines. This division between curricular areas may serve as a hindrance to students' long-term learning and their ability to generalize. In contrast, cross-curricular pedagogy provides a way for students to think beyond the classroom walls and make important connections across disciplines. The purpose of this paper is a theoretical reflection on our use of Expansive Framing in our design of lessons across learning environments within the school. We provide a narrative account of our early work in using this theoretical framework to co-plan and enact …