Structure Identification For High-Dimensional Data In The Vicinity Of Bear Lake,
2024
Utah State University
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,
2024
Faculty of Science
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,
2024
Faculty of Science
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,
2024
Faculty of Science
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,
2024
คณะวิทยาศาสตร์
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,
2024
Faculty of Science
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,
2024
คณะวิทยาศาสตร์
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,
2024
Faculty of Science
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,
2024
คณะวิทยาศาสตร์
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,
2024
Faculty of Science
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,
2024
Faculty of Science
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,
2024
Faculty of Science
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,
2024
Faculty of Science
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,
2024
Faculty of Science
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,
2024
Utah State University
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 …
On Combinatorics Of Voronoi Polytopes For Perturbations Of The Dual Root Lattices,
2024
The University of Texas Rio Grande Valley
On Combinatorics Of Voronoi Polytopes For Perturbations Of The Dual Root Lattices, Alexey Garber
School of Mathematical & Statistical Sciences Faculty Publications
The Voronoi conjecture on parallelohedra claims that for every convex polytope P that tiles Euclidean d-dimensional space with translations there exists a d-dimensional lattice such that P and the Voronoi polytope of this lattice are affinely equivalent. The Voronoi conjecture is still open for the general case but it is known that some combinatorial restrictions for the face structure of P ensure that the Voronoi conjecture holds for P. In this article, we prove that if P is the Voronoi polytope of one of the dual root lattices Dd*, E6*, E7* or E8*=E8 or their small perturbations, then every parallelohedron …
Logarithmic Algorithms For Fair Division Problems,
2024
The University of Texas Rio Grande Valley
Logarithmic Algorithms For Fair Division Problems, Alexandr Grebennikov, Xenia Isaeva, Andrei V. Malyutin, Mikhail Mikhailov, Oleg R. Musin
School of Mathematical & Statistical Sciences Faculty Publications
We study the algorithmic complexity of fair division problems with a focus on minimizing the number of queries needed to find an approximate solution with desired accuracy. We show for several classes of fair division problems that under certain natural conditions on sets of preferences, a logarithmic number of queries with respect to accuracy is sufficient.
Deep Neural Networks: A Formulation Via Non-Archimedean Analysis,
2024
The University of Texas Rio Grande Valley
Deep Neural Networks: A Formulation Via Non-Archimedean Analysis, Wilson A. Zuniga-Galindo
School of Mathematical & Statistical Sciences Faculty Publications
We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified using numbers from the ring of integers of non-Archimdean local fields. These rings have a natural hierarchical organization as infinite rooted trees. Natural morphisms on these rings allow us to construct finite multilayered architectures. The new DNNs are robust universal approximators of real-valued functions defined on the mentioned rings. We also show that the DNNs are robust universal approximators of real-valued square-integrable functions defined in the unit interval.
On The Center And The Antipode Of The Super-Yangian Of Q(1),
2024
The University of Texas Rio Grande Valley
On The Center And The Antipode Of The Super-Yangian Of Q(1), Elena Poletaeva
School of Mathematical & Statistical Sciences Faculty Publications
For the queer Lie superalgebra Q(1), we explicitly describe the center of the super-Yangian Y Q(1) of Q(1) in terms of generators of Y Q(1). We also describe the square of the antipodal map on Y Q(1) and use the antipode to construct an involutive automorphism of Y Q(1).
Conditional Constrained And Unconstrained Quantization For Probability Distributions,
2024
The University of Texas Rio Grande Valley
Conditional Constrained And Unconstrained Quantization For Probability Distributions, Megha Pandey, Mrinal Kanti Roychowdhury
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we present the idea of conditional quantization for a Borel probability measure P on a normed space Rk. We introduce the concept of conditional quantization in both constrained and unconstrained scenarios, along with defining the conditional quantization errors, dimensions, and coefficients in each case. We then calculate these values for specific probability distributions. Additionally, we demonstrate that for a Borel probability measure, the lower and upper quantization dimensions and coefficients do not depend on the conditional set of the conditional quantization in both constrained and unconstrained quantization.
