Mathematics Commons^™

Stochastic Differential Equation Models On Sphere For Animal Migration, Viput Puttanugool

Chulalongkorn University Theses and Dissertations (Chula ETD)

Animal migration is a seasonal movement of a bundle of animals from place to place. A migration cycle is often annually and closely linked with the cyclic pattern of seasons. A short-distance migration can be modeled on a planar surface, but most animals have long-distance migrations, e.g., Arctic terns migrate from the North Pole to the South Pole; thus, their migration should be modeled on a spherical surface. In addition, the Brownian motion term is included in a model to represent noises and randomness of movements. This work aims to simulate their migration routes using stochastic differential equations (SDEs) on …

Improved Adaptive Fractional Order Differential Method For Medical Image Enhancement, Wasin Tranghiranyathorn

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this work, we propose a construction of a new 5x5 fractional order differential mask that uses sixteen directions of gradient operator and weights each pixel in the mask by the Euclidean distance from the center of the mask. Then, we apply this new mask to the Adaptive Fractional Differential Algorithm (AFDA). The AFDA allows the optimal fractional order of each pixel to be obtained using an adaptive function constructed based on the area feature of image. Experimental results for medical images, show that the AFDA with the new mask gives better image enhancement than the original AFDA. It makes …

Knight's Tours On Ringboards, Deficient 4 X N Chessboards And Some L-Boards, Wasupol Srichote

Chulalongkorn University Theses and Dissertations (Chula ETD)

A (legal) knight's move is the result of moving the knight two squares horizontally or vertically on the board and then turning and moving one square in a perpendicular direction. A closed knight's tour is a sequence of knight's moves that visits every square on a given chessboard exactly once and returns to its start square. A closed knight's tour and its variations are studied widely over the rectangular chessboard or a three-dimensional rectangular box. For m,n > 2r, an (m,n,r)-ringboard or RB(m,n,r) is defined to be an m x n chessboard, denoted by CB(m x n), with the middle part …

Discrete-Time Risk Model Based On Zero Inflated Poisson Time Series, Siwarak Sawongnam

Chulalongkorn University Theses and Dissertations (Chula ETD)

An important goal of actuary is to develop models for company portfolio and insurance products. Risk measurement is one of the essential measures that inform actuaries and risk managers about the degree to which the risk bearing entity. To have precise risk measure, we require an appropriate claim count process. The common claim count processes are usually constructed from the Poisson distribution. However, insurance data have generally excess zeros which causes the overdispersion. This violates the assumption of the Poisson distribution. Therefore, alternative distributions accommodating zero count are explored in literature. The zero inflated Poisson distribution is one of the …

Positive Labeled And Unlabeled Learning Methods Of Meta-Path Based Functional Profiles For Predicting Drug-Disease Associations, Thitipong Kawichai

Chulalongkorn University Theses and Dissertations (Chula ETD)

Drug repositioning, discovering new indications for existing drugs, is a competent strategy to reduce time, costs, and risk in drug discovery and development. Many computational methods have been developed to identify new drug-disease associations for further validation and drug development. A recent approach showing superior performance with less required data is a meta-path based approach, which derives network-based information using path patterns from drug to disease nodes. However, existing meta-path based methods discard information of intermediate nodes along paths, which are important indicators for describing relationships between drugs and diseases. With known (positive) and unknown (unlabeled) drug-disease associations, this research …

Quaternion Algebras Over Some Extensions Of Function Fields, Silipong Thongmeepun

Chulalongkorn University Theses and Dissertations (Chula ETD)

In this thesis, we study quaternion algebras over rational function fields over finite fields of odd order. [It is known that a quaternion algebra is either the algebra of 2x2- matrices or a division algebra.] We determine conditions for quaternion algebras of the form(symbol) to be division algebras and conditions for quaternion algebras to split after the constant quadratic field extension.

Effects Of Aperiodicity And Frustration On The Magnetic Properties Of Artificial Quasicrystals, Barry Farmer

Theses and Dissertations--Physics and Astronomy

Quasicrystals have been shown to exhibit physical properties that are dramatically different from their periodic counterparts. A limited number of magnetic quasicrystals have been fabricated and measured, and they do not exhibit long-range magnetic order, which is in direct conflict with simulations that indicate such a state should be accessible. This dissertation adopts a metamaterials approach in which artificial quasicrystals are fabricated and studied with the specific goal of identifying how aperiodicity affects magnetic long-range order. Electron beam lithography techniques were used to pattern magnetic thin films into two types of aperiodic tilings, the Penrose P2, and Ammann-Beenker tilings. SQUID …

Statistical Analysis Of Demographic Effects On Insurance Coverage Of Perinatal And Neonatal Morbidity, Madeline Durbin

Undergraduate Honors Thesis Projects

In the United States of America, Ohio has one of the worst neonatal and perinatal death rates. Within Ohio, Montgomery County has an above average neonatal and perinatal death rate. This statistic can be lowered if more women in Montgomery County have health insurance. They would be more likely to seek out prenatal health care, since they would no longer have to pay as much money out-of-pocket. This would allow medical professionals to be able to diagnose and treat any potential issues in the mother or child earlier. Having health insurance would also prevent mothers-to-be from seeking out other potentially …

Symmetry Algebras Of The Canonical Lie Group Geodesic Equations In Dimension Five, Hassan Almusawa

Theses and Dissertations

Nowadays, there is much interest in constructing exact analytical solutions of differential equations using Lie symmetry methods. Lie devised the method in the 1880s. These methods were substantially developed utilizing modern mathematical language in the 1960s and 1970s by several different groups of authors such as L.V. Ovsiannikov, G. Bluman, and P. J. Olver, and have since been implemented as a software package for symbolic computation on commonly used platforms such as Mathematica and MAPLE.

In this work, we first develop an algorithmic scheme using the MAPLE platform to perform a Lie symmetry algebra identification and validate it on nonlinear …

Invariance And Invertibility In Deep Neural Networks, Han Zhang

Theses and Dissertations

Machine learning is concerned with computer systems that learn from data instead of being explicitly programmed to solve a particular task. One of the main approaches behind recent advances in machine learning involves neural networks with a large number of layers, often referred to as deep learning. In this dissertation, we study how to equip deep neural networks with two useful properties: invariance and invertibility. The first part of our work is focused on constructing neural networks that are invariant to certain transformations in the input, that is, some outputs of the network stay the same even if the input …

Visualizing The Mean And The Standard Deviation Using R/Rstudio Shiny Package, Rachel Hufnagel, Ziyi Chen, Mamunur Rashid, Jyotirmoy Sarkar

Student Research

Many of us have experienced an unpleasant situation in which only the mean and the standard deviation of a data set are reported, but we are expected to know everything about the dataset as if those two values were all we needed to know. We would learn so much more if there were easy ways to create and share graphical representations and interpretations of the entire raw data. In this paper, we not only explain what the mean and the standard deviation tell us about a data set, but also describe how to include additional information on the data. We …

Fuzzy Logistic Regression For Detecting Differential Dna Methylation Regions, Tarek M. Bubaker Bennaser

Doctoral Dissertations

“Epigenetics is the study of changes in gene activity or function that are not related to a change in the DNA sequence. DNA methylation is one of the main types of epigenetic modifications, that occur when a methyl chemical group attaches to a cytosine on the DNA sequence. Although the sequence does not change, the addition of a methyl group can change the way genes are expressed and produce different phenotypes. DNA methylation is involved in many biological processes and has important implications in the fields of biomedicine and agriculture.

Statistical methods have been developed to compare DNA methylation at …

Explicit Determinantal Formula For A Class Of Banded Matrices, Yerlan Amanbek, Zhibin Du, Yogi Erlangga, Carlos M. Da Fonseca, Bakytzhan Kurmanbek, António Pereira

All Works

© 2020 Yerlan Amanbek et al., published by De Gruyter 2020. In this short note, we provide a brief proof for a recent determinantal formula involving a particular family of banded matrices.

On Cohen-Macaulay Hopf Monoids In Species, Jacob A. White

School of Mathematical & Statistical Sciences Faculty Publications

We study Cohen-Macaulay Hopf monoids in the category of species. The goal is to apply techniques from topological combinatorics to the study of polynomial invariants arising from combinatorial Hopf algebras. Given a polynomial invariant arising from a linearized Hopf monoid, we show that under certain conditions it is the Hilbert polynomial of a relative simplicial complex. If the Hopf monoid is Cohen- Macaulay, we give necessary and sufficient conditions for the corresponding relative simplicial complex to be relatively Cohen-Macaulay, which implies that the polynomial has a nonnegative h-vector. We apply our results to the weak and strong chromatic polynomials of …

A Mathematical Model For Visco-Ferromagnetic Materials, Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden

Articles

Visco-ferromagnetic materials represented by non-local constitutive equation are considered in the paper. We use fractional derivatives in order to describe memory and spatial effects. Also, thermodynamic principles are formulated and studied.

Numerical Modeling Of Submicron Particles For Acoustic Concentration In Gaseous Flow, Jizhou Liu, Xiaodong Li, Fang Q. Hu

Mathematics & Statistics Faculty Publications

This paper intends to explore the rationality and feasibility of modeling dispersed submicron particles in air by a kinetic-based method called the unified gas-kinetic scheme (UGKS) and apply it to the simulation of particle concentration under a transverse standing wave. A gas-particle coupling scheme is proposed where the gas phase is modeled by the two-dimensional linearized Euler equations (LEE) and, through the analogous behavior between the rarefied gas molecules and the air-suspended particles, a modified UGKS is adopted to estimate the particle dynamics. The Stokes' drag force and the acoustic radiation force applied on particles are accounted for by introducing …

Classification Models Of Idiopathic Pulmonary Fibrosis Patients, Mohammed Alqawba, Luis R. Rodriguez, Norou Diawara, Rebecca T. Beuschel, Maryann Kaler, Amisha V. Barochia, Stewart J. Levine, Steven D. Nathan, Geraldine Grant

Mathematics & Statistics Faculty Publications

Idiopathic pulmonary fibrosis (IPF) is a chronic and fatal interstitial lung disease with no current cure. Progression of IPF is difficult to predict as the clinical course can be highly variable and range from a rapidly deteriorating state to a relatively stable state, or may be characterized by a slow progressive decline. Therefore, the need for an accurate diagnosis and improved tools for monitoring and managing IPF is of paramount importance, all for understanding the mitochondrial structure and the function played in the IPF. Mitochondrial DNA copy number (MtDCN) has been correlated with mortality in IPF patients and is a …

What's Your Sphericity Index? Rationalizing Surface Area And Volume, John A. Adam

Mathematics & Statistics Faculty Publications

Virginia Standards of Learning include mathematical content related to the surface area and the volume of various geometric objects. In the seventh grade, “Students... solve problems involving volume and surface area” In the eighth grade, “Proportional reasoning is expounded upon as students solve a variety of problems. Students find the volume and surface area of more complex three dimensional figures”. In high school geometry, “The student... use[s] surface area and volume of three-dimensional objects to solve practical problems” (Virginia Department of Education, 2016). The challenge is to find scenarios that are engaging to students and keep them interested in the …

Analysis On Sharp And Smooth Interface, Elizabeth V. Hawkins

College of Graduate Studies: Theses & Dissertations

In biology, minimizing a free energy functional gives an equilibrium shape that is the most stable in nature. The formulation of these functionals can vary in many ways, in particular they can have either a smooth or sharp interface. Minimizing a functional can be done through variational calculus or can be proved to exist using various analysis techniques. The functionals investigated here have a smooth and sharp interface and are analyzed using analysis and variational calculus respectively. From the former we find the condition for extremum and its second variation. The second variation is commonly used to analyze stability of …

Artificial Neural Network Models For Pattern Discovery From Ecg Time Series, Mehakpreet Kaur

College of Graduate Studies: Theses & Dissertations

Artificial Neural Network (ANN) models have recently become de facto models for deep learning with a wide range of applications spanning from scientific fields such as computer vision, physics, biology, medicine to social life (suggesting preferred movies, shopping lists, etc.). Due to advancements in computer technology and the increased practice of Artificial Intelligence (AI) in medicine and biological research, ANNs have been extensively applied not only to provide quick information about diseases, but also to make diagnostics accurate and cost-effective. We propose an ANN-based model to analyze a patient's electrocardiogram (ECG) data and produce accurate diagnostics regarding possible heart diseases …