Hyperparameter Estimation For Sparse Bayesian Learning Models,
2024
University of Minnesota
Hyperparameter Estimation For Sparse Bayesian Learning Models, Feng Yu, Lixin Shen, Guohui Song
Mathematics & Statistics Faculty Publications
Sparse Bayesian learning (SBL) models are extensively used in signal processing and machine learning for promoting sparsity through hierarchical priors. The hyperparameters in SBL models are crucial for the model’s performance, but they are often difficult to estimate due to the nonconvexity and the high-dimensionality of the associated objective function. This paper presents a comprehensive framework for hyperparameter estimation in SBL models, encompassing well-known algorithms such as the expectation-maximization, MacKay, and convex bounding algorithms. These algorithms are cohesively interpreted within an alternating minimization and linearization (AML) paradigm, distinguished by their unique linearized surrogate functions. Additionally, a novel algorithm within the …
Shadow Hands,
2024
Old Dominion University
Shadow Hands, John Adam
Mathematics & Statistics Faculty Publications
The article titled "Shadow hands" discusses a statement made by authors Dave Lynch and Bill Livingston in their book "Color and Light in Nature." The authors state that when you cast a shadow with your hand onto a piece of paper, the sharpness of the shadow's edge diminishes as you raise your hand above the surface. This fuzzy outer edge of the shadow is called the penumbra, and its width divided by its distance from your hand is always a constant fraction of about 1/112. The article poses two questions related to this statement and asks readers to explain it …
Pigeon Strike!: Solutions For Fermi Questions, October 2024,
2024
Old Dominion University
Pigeon Strike!: Solutions For Fermi Questions, October 2024, John Adam
Mathematics & Statistics Faculty Publications
This article, titled "Pigeon strike!: Solutions for Fermi Questions, October 2024," discusses the estimation of various physics-related questions regarding a pigeon striking a window. The author estimates the momentum and kinetic energy of the bird prior to hitting the window, as well as the force, pressure, and wingspan of the bird during impact. The author assumes an inelastic collision between the bird and the window, and provides calculations and explanations for their estimations. The article concludes with the author's observation that the estimated wingspan aligns with that of an adult pigeon.
On Graph Decompositions And Designs: Exploring The Hamilton-Waterloo Problem With A Factor Of 6-Cycles And Projective Planes Of Order 16,
2024
Michigan Technological University
On Graph Decompositions And Designs: Exploring The Hamilton-Waterloo Problem With A Factor Of 6-Cycles And Projective Planes Of Order 16, Zazil Santizo Huerta
Dissertations, Master's Theses and Master's Reports
This dissertation tackles the challenging graph decomposition problem of finding solutions to the uniform case of the Hamilton-Waterloo Problem (HWP). The HWP seeks decompositions of complete graphs into cycles of specific lengths. Here, we focus on cases with a single factor of 6-cycles. The dissertation then delves into the construction of 1-rotational designs, a concept from finite geometry. It explores the connection between these designs and finite projective planes, which are specific geometric structures. Finally, the dissertation proposes a potential link between these seemingly separate areas. It suggests investigating whether 1-rotational designs might hold the key to solving unsolved instances …
Modeling Inflation Using A Fast Fourier Transform (Fft),
2024
The University of Akron
Modeling Inflation Using A Fast Fourier Transform (Fft), Blake Smith
Williams Honors College, Honors Research Projects
This paper utilizes a Fast Fourier Transform (FFT) algorithm to construct a trigonometric interpolant for the Consumer Price Index (CPI), which is then differentiated and used to obtain a continuous function for “instantaneous” (i.e., month-wise) inflation, as opposed to a 12-month percent-change. Fourier coefficients are analyzed to investigate underlying periodicities in the newly constructed function. This metric does not hold significant predictive value but it may prove helpful in retroactive analysis of inflation trends.
L∞ Bounds For Transient Growth In Repetitive And Iterative Learning Control Systems,
2024
Missouri University of Science and Technology
L∞ Bounds For Transient Growth In Repetitive And Iterative Learning Control Systems, Douglas A. Bristow, John R. Singler
Mechanical and Aerospace Engineering Faculty Research & Creative Works
This paper revisits the problem of large transient growth in Iterative Learning Control (ILC) and Repetitive Process Control (RPC) systems. In ILC and RPC problems a process is repeated iteratively, with new control calculations occurring in between each iteration. Large transient growth refers to the propensity of some control algorithms to grow error exponentially before eventually converging. While robust monotonic convergence algorithms (in which monotonic convergence is guaranteed usually in exchange for a small loss in performance) have largely eliminated the concern for large transient growth in ILC, similar results cannot always be obtained in RPC. The emergence of additive …
Frieze And Tiling Groups In The Lorentz-Minkowski Plane,
2024
University of Central Florida
Frieze And Tiling Groups In The Lorentz-Minkowski Plane, Michael O. Lynch
Honors Undergraduate Theses
In this thesis, there is a presentation of the isometries from the Lorentz-Minkowski Plane and a solution to the Frieze Patterns. There is a suggestion for a solution for the Tiling Patterns. Since the construction of these mathematical structures is well understood in the Euclidean plane, one can follow a similar approach to the construction of such objects to find the unique number of groups that describe all possible frieze patterns while there is a suggestion of the number for the tiling case. There is a reflection of these results in a computational and cosmological context.
Refining The Inverse Lipschitz Constant For Injective Relu Networks,
2024
South Dakota State University
Refining The Inverse Lipschitz Constant For Injective Relu Networks, Cole Rausch
Electronic Theses and Dissertations
In this thesis, we study the Inverse Lipschitz Constant (ILC) of injective ReLU layers. We study the tightness of the ILC lower bound established in Puthawala et al. Our approach has three components. First, we find that the conditions for injectivity on lines yield a weaker condition than the general condition given in Puthawala et al. Second, we perform numerical experiments to judge the tightness of the existing ILC lower bound and find that bound is overly conservative. Third, we identify the source of the potential slack in the proof of the existing ILC bound, and perform further numerical experiments …
Linear Topological Space,
2024
University of North Florida
Linear Topological Space, Vi Nguyen
UNF Graduate Theses and Dissertations
This thesis begins with an introduction to linear and topological spaces and then defines linear topological spaces. It studies key properties such as neighborhoods, convexity, reflexivity, and weak and weak* topologies. Finally, it concludes with solving non-linear partial differential equations.
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 …
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- …
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 …
