Digital Commons Network^™

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

Bridging Theory And Application: A Journey From Minkowski's Theorem To Ggh Cryptosystems In Lattice Theory, Danzhe Chen

CMC Senior Theses

This thesis provides a comprehensive exploration of lattice theory, emphasizing its dual significance in both theoretical mathematics and practical applications, particularly within computational complexity and cryptography. The study begins with an in-depth examination of the fundamental properties of lattices and progresses to intricate lattice-based problems such as the Shortest Vector Problem (SVP) and the Closest Vector Problem (CVP). These problems are analyzed for their computational depth and linked to the Subset Sum Problem (SSP) to highlight their critical roles in understanding computational hardness. The narrative then transitions to the practical applications of these theories in cryptography, evaluating the shift from …

Instances Of Undecidability In The Semigroup Word Problem, Timothy C. Grosky

Honors Theses and Capstones

We will examine the decidability of the word problem in semigroups, which is a yes/no question. We will examine tools that have been developed to help answer it, and then look at some examples where the word problem is decidable or undecidable.

Machine Learning Approaches For Cyberbullying Detection, Roland Fiagbe

Data Science and Data Mining

Cyberbullying refers to the act of bullying using electronic means and the internet. In recent years, this act has been identifed to be a major problem among young people and even adults. It can negatively impact one’s emotions and lead to adverse outcomes like depression, anxiety, harassment, and suicide, among others. This has led to the need to employ machine learning techniques to automatically detect cyberbullying and prevent them on various social media platforms. In this study, we want to analyze the combination of some Natural Language Processing (NLP) algorithms (such as Bag-of-Words and TFIDF) with some popular machine learning …

Rupert Property Of Some Solids In Higher Dimensions, Pongbunthit Tonpho

Chulalongkorn University Theses and Dissertations (Chula ETD)

We say that a solidS has the Rupert property if a hole could be cut into one copy of S so that another copy of S can be passed through this hole. In recent years, many solids in R$ have been shown to have the Rupert property. However, not much is known about the Rupert property in higher dimensions. This dissertation investigates the Rupert property for some solids in R". We introduce lemmas that help to verify this property. In particular, we prove that some particular n-simplices, the generalized n-octahedrons/and the two-way cones in In have the Rupert property.

Splitness Of The Characteristic Polynomial Of 2×2 Normal Matrices Over A Finite Field, Sarawut Therdchanthuk

Chulalongkorn University Theses and Dissertations (Chula ETD)

เราได้ทฤษฎีบทสเปกตรัมสำหรับเมทริกซ์ขนาด 2x2 เหนือฟีลด์จำกัดที่มีลักษณะเฉพาะเท่ากับ 2 โดยการตรวจสอบการแตกตัวของพหุนามลักษณะเฉพาะเหนือฟีลด์ดังกล่าว ซึ่งใช้ข้อเท็จจริงเสริมบางประการเกี่ยวกับพหุนามกำลังสองและเมทริกซ์เหนือฟีลด์ดังกล่าว พหุนามลักษณะเฉพาะจะสะท้อนให้เห็นถึงรูปแบบบัญญัติของเมทริกซ์เหล่านี้ เป็นผลให้สามารถแยกชั้นความคล้ายของเมทริกซ์ปรกติได้ และสำหรับเมทริกซ์ปรกติที่แปลงเป็นทแยงมุมได้ เราให้ข้อความที่สมมูลกับการทำให้เป็นเมทริกซ์ที่แปลงเป็นทแยงมุมแบบยูนิแทรีได้

Developing Test Statistics For Familial Dna Searches Through Multinomial Logistic Regression Model, Akaraphon Jantaraphum

Chulalongkorn University Theses and Dissertations (Chula ETD)

In hypothesis testing for familial DNA searches, the likelihood ratio (LR) is a commonly used statistic that requires allele frequency distributions. However, since the population background of a forensic sample is generally unknown, the appropriate allele frequency distribution is uncertain. To address this issue, various LR-based methods—such as those using local allele frequencies (LRLAF), or selecting maximum, minimum, or average LRs (LRMAX, LRMIN, LRAVG), and Naive Bayes classification (LRNB)—have been developed. In this study, we introduce a family of LR-based statistics incorporating multinomial logistic regression classification (LRMLR). DNA samples are classified into subpopulations using multinomial logistic regression, and the likelihood …

Two-Step-Change Pivot Rule For Simplex Method, Rawit Chaiareekij

Chulalongkorn University Theses and Dissertations (Chula ETD)

The simplex method is a fundamental method for solving linear programming problems proposed by George B. Dantzig in 1963. The simplex method’s efficiency hinges on the choice of the entering variable, determined by the pivot rule. Dantzig’s original pivot rule, while effective in many cases, can exhibit exponential behavior on certain problems. To address this problem, this thesis proposes a new pivot rule for the simplex method, called the two-step-change pivot rule. The idea is to obtain the two-step-change improvement from the objective value by computing the direction of change for each entering variable to determine the cost per unit. …

Key Factor Analysis For Base Patterns In Minibridge By Reinforcement Learning, Thanathat Dechakulkamjorn

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.

Specifying The Desired Attributes Of Solutions To Vehicle Routing Problems With Time Windows Using Machine Learning, Teerapong Chaochanglek

Chulalongkorn University Theses and Dissertations (Chula ETD)

A vehicle routing problem with time windows (VRPTW) has been studied widely in the literature. Most effective methods to find a solution are still heuristics, which are constructed from the inventor’s ideas of how a good solution should be obtained, and their efficiency is quantified only by empirical data. However, these ideas may or may not yield a near-optimal solution. It would be better if we can identify some characteristics of a solution to VRPTW to help guide the heuristic in the right direction. Arnold and Sörensen had proposed a statistical learning model to determine a characteristic of a near-optimal …

Closed-Form Formulas For Conditional Moments Of Stochastic Volatility Markovswitching Model And Applications, Supavit Kiatteerarat

Chulalongkorn University Theses and Dissertations (Chula ETD)

In the present day, the regime-switching model plays a crucial role in the financial world. This thesis studies a stochastic volatility model with regime switching, specifically examining a Markovian regime-switching process known as Cox-Ingersoll-Ross. Analytical formulas for the conditional moment generation function of the process are developed, presenting both a linearly closed-form and an exponentially closed-form. The formulas are derived by solving a partial differential equation (PDE) that obtains the Feynman-Kac Theorem. We also present the relationship between these two closed-forms, demonstrated by using the formula by Faà Bruno. Additionally, a numerical validation, the Monte Carlo method, is employed to …

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 …

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.

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.

Enhancing Set-Theoretic Research Methods With Neutrosophic Sets, Maikel Yelandi Leyva Vázquez, Jesús Estupiñán Ricardo, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This study employed the integration of neutrosophic set theory with set-theoretic methods and Qualitative Comparative Analysis (QCA) to examine intricate social phenomena. Participants' opinions and attitudes were captured using neutrosophic Likert scales, which reflected elements of truth, indeterminacy, and falsity. This proposal is illustrated in a case study facilitated a more comprehensive and subtle examination, emphasizing the significance of variables such as motivation, instructional excellence, and educational resources in achieving academic accomplishment. The results of the necessary condition analysis and set coincidence analysis indicated that motivation and teaching quality have the highest individual impact. Nevertheless, the convergence of scholarly resources, …

Foundation Of Appurtenance And Inclusion Equations For Constructing The Operations Of Neutrosophic Numbers Needed In Neutrosophic Statistics Foundation Of Appurtenance And Inclusion Equations For Constructing The Operations Of Neutrosophic Numbers Needed In Neutrosophic Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We introduce for the first time the appurtenance equation and inclusion equation, which help in understanding the operations with neutrosophic numbers within the frame of neutrosophic statistics. The way of solving them resembles the equations whose coefficients are sets (not single numbers).

Legendrian Torus And Cable Links, Jennifer Dalton,, John B. Etnyre, Lisa Traynor

Mathematics Faculty Research and Scholarship

We give a classification of Legendrian torus links. Along the way, we give the first classification of infinite families of Legendrian links where some smooth symmetries of the link cannot be realized by Legendrian isotopies. We also give the first family of links that are non-destabilizable but do not have maximal Thurston-Bennequin invariant and observe a curious distribution of Legendrian torus knots that can be realized as the components of a Legendrian torus link. This classification of Legendrian torus links leads to a classification of transversal torus links.

We also give a classification of Legendrian and transversal cable links of …

Improveing F-Beta Score In Classifying Shark Data Into Shark Behaviors, Ibrahim M. Ali

CGU Theses & Dissertations

One metric used to measure classification performance in machine learning is F-beta score. The objective in this thesis is to improve the average F-b score computed in classifying shark data into shark behaviors, namely; Resting, Swimming, Feeding, and Non-Directed Motion (NDM). Synthetic Minority Oversampling Technique (SMOTE) and Adaptive Synthetic Sampling (ADASYN) are utilized to balance the data, from which pre-processed Fast Fourier Transform (FFT), Walsh-Hadamard Transform (WHT), and Autocorrelation (AC) features are extracted then classified using Convolutional Neural Network (CNN) and K-Nearest Neighbors (K-NN). All the combinations of the two balancing techniques, the three feature types, and the two machine …

Ncmpy: A Modelling Software For Neutrosophic Cognitive Maps Based On Python Package, Ilanthenral Kandasamy, Divakar Arumugam, Aryan Rathore, Ateeth Arun, Manan Jain, Vasantha Kandasamy, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Cognitive Maps are a vital tool that can be used for knowledge representation and reasoning. Fuzzy Cognitive Maps (FCMs) are popular soft computing techniques used to model large and complex systems, and they can aid in explainable AI. FCMs, however, cannot model the indeterminacy that arises in a system due to various uncertainties. Neutrosophic Cognitive Maps (NCMs), upgraded FCMs that could model indeterminacy, was introduced to address this issue. NCMs are a generalization of FCMs, a field of cognitive science firmly based on neural networks. NCMs have been used to solve a wide range of problems. NCMs were introduced in …

A Decision-Making Approach Incorporating Todim Method And Sine Entropy In Q-Rung Picture Fuzzy Set Setting, Büşra Aydoğan, Murat Olgun, Florentin Smarandache, Mehmet Unver

Branch Mathematics and Statistics Faculty and Staff Publications

In this study, we propose a new approach based on fuzzy TODIM (Portuguese acronym for interactive and multicriteria decision-making) for decision-making problems in uncertain environments. Our method incorporates group utility and individual regret, which are often ignored in traditional multicriteria decision-making (MCDM) methods. To enhance the analysis and application of fuzzy sets in decision-making processes, we introduce novel entropy and distance measures for q-rung picture fuzzy sets. These measures include an entropy measure based on the sine function and a distance measure derived from the Jensen-Shannon divergence. In our methodology, incorporating the sine function into the entropy measure stands out …

Super Hiper Funcion Y Super Hiper Estructura Y Sus Correspondientes Super Hiper Funcion Neutrosofica Y Super Hiper Estructura Neutrosofica, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

El n-ésimo Conjunto Potencia de un Conjunto {o Pn(S)} describe mejor nuestro mundo real, porque un sistema S (que puede ser una empresa, institución, asociación, país, sociedad, conjunto de objetos/plantas/animales/seres, conjunto de conceptos/ideas/proposiciones, etc.) está formado por subsistemas, que a su vez están formados por sub-subsistemas, y así sucesivamente. Demostramos que la Super Hiper Función es una generalización de la Función clásica, Super Función y la Hiper Función. Y el Super Hiper Álgebra, Super Hiper Gráfico son parte de la Super Hiper Estructura. Casi todas las estructuras en nuestro mundo real son Super Hiper Estructuras Neutrosóficas ya que tienen …

Prefacio Del Número Especial Sobre La Aplicación De La Neutrosófica En Latinoamérica, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

En un mundo caracterizado por la complejidad y la incertidumbre, los marcos de pensamiento que pueden abrazar la ambigüedad y el conflicto inherente a nuestras vidas son de un valor incalculable. La neutrosófica, con su compromiso de explorar el espacio entre el verdadero y el falso, ha emergido como una perspectiva poderosa y transformadora en el ámbito académico y profesional. Este número especial de Investigación Operacional es un testimonio del creciente interés y de la aplicación de la neutrosófica en Latinoamérica, un continente diverso y vibrante que enfrenta desafíos únicos y oportunidades en el siglo XXI.

Neutrosophie : Un Cadre Interdisciplinaire Pour Une Meilleure Compréhension De L’Incertitude Et De L’Indétermination, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

La neutrosophie, un cadre philosophique et scientifique relativement récent introduit dans les années 1990,1 propose une approche robuste pour comprendre et modéliser l’indétermination, la contradiction et l’incertitude. Explorons les concepts fondamentaux de la neutrosophie et quelques diverses applications à travers plusieurs disciplines, notamment les mathématiques, la physique, la sociologie, la psychologie et la biologie.

Nuevos Tipos De Conjuntos Suaves: Conjunto Hiper Suave, Conjunto Suave Indeterminado, Conjunto Hiper Suave Indeterminado Y Conjunto Suave De Árbol, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This is an updated article, where we present the definitions and practical applications of the Soft Set and its extensions to the Hyper Soft Set, Indeterminate Soft Set, Indeterminate Hyper Soft Set, and Tree Soft Set.

Análisis Neutrosófico De Las Actitudes Hacia La Máquina De Experiencia De Nozick, Maikel Yelandi Leyva Vázquez, Jesús Estupiñán Ricardo, Noel Batista Hernández, Ricardo Sánchez Casanova, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper presents a neutrosophic study on attitudes towards virtual technology, with a special focus on the "Experience Machine". Employing a methodology that incorporates the theory of indecision and neutrality into response analysis, the perceptions of 50 university students were investigated. Opinions and feelings were transformed into neutrosophic numbers to calculate contradiction and conduct a detailed analysis. The results indicate a predisposition towards agreement with virtual technology, although notable indecision and a significant presence of neutral attitudes were detected. The correlations and clustering methods applied reveal a complex dynamic of attitudes, challenging binary interpretations and highlighting the need for more …

Two-Dimensional Steady Squeezing Flow Over A Vertical Porous Channel With Free Convective Heat/Mass Transfer And Invariable Suction, Zeeshan, Waris Khan, Taoufik Saidani, Florentin Smarandache, Muhammad Shahid Khan, Hamdi Ayed, M. Modather M. Abdou

Branch Mathematics and Statistics Faculty and Staff Publications

This research reports on the combined effects of heat and mass transfer (HMT) under the influences of the Soret and Dufour in natural convection steady 2D magnetohydrodynamic flow through the boundary layer in a porous vertical tube or duct. The current study is motivated by the significant applications of HMT in engineering processes such as casting and welding. The goal of this framework is to explore the assisting and opposing movements with HMT above a vertical porous channel under the influence of invariant suction and fluid dissipation which have not been reported in the earlier studies. The governing flow equations …

Progress In Physics: Twentieth Year Of Publication, Florentin Smarandache, Andreas Ries, Pierre Millette, Ebenezer Chifu

Branch Mathematics and Statistics Faculty and Staff Publications

The journal Progress in Physics was created in January 2005 on behalf of many influential scientists with whom we were in correspondence. The main reason was that publications in other journals were allowed only if the submitter was affiliated with a scientific institution or research organization. Given this situation, many working scientists finding themselves partially employed or unemployed, such as in between research grants, find themselves unable to publish their research results. Even e-print archives such as Cornell’s arXiv required scientific affiliation and still follow this policy.

Neutrosophic Discrete Geometric Distribution, Rehan Ahmad Khan Sherwani, Sadia Iqbal, Shumaila Abbas, Muhammad Saleem, Muhammad Aslan, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Uncertainty, vagueness, and ambiguity surround us in many real-life problems and, therefore, always remain under consideration for researchers to quantify them. This study proposed neutrosophic discrete probability distribution as a generalization of classical or existing probability distributions, named neutrosophic geometric distribution. Case studies presented in the paper will help understand the concept and application of the proposed distribution. Several properties are derived, like the proposed distribution’s moment, characteristic, and probability-generating functions. Furthermore, the newly proposed distribution derives properties from the reliability analysis, such as survival function, hazard rate function, reversed hazard rate function, cumulative hazard rate function, mills ratio, and …

Many Extensions Of Coulomb’S Law: A Scoping Review, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, Coulomb’s Law is extended from two stationary charged particles, on linear trajectory, to: many charged particles, or quantum level particles, or objects on arbitrary motions (with velocity, acceleration, time delay), on non-linear trajectories, at even superluminal and instantaneous speeds.