Mathematics Commons^™

On The Planarity Of Generalized Line Graphs, Khawlah H. Alhulwah, Mohra Zayed, Ping Zhang

Theory & Applications of Graphs

One of the most familiar derived graphs is the line graph. The line graph L(G) of a graph G is that graph whose vertices are the edges of G where two vertices of L(G) are adjacent if the corresponding edges are adjacent in G. Two nontrivial paths P and Q in a graph G are said to be adjacent paths in G if P and Q have exactly one vertex in common and this vertex is an end-vertex of both P and Q. For an integer ℓ ≥ 2, the ℓ -line graph Lℓ (G) of a …

On Numerical Stochastic Optimal Control Via Bellman's Dynamic Programming Principle, Prince Osei Aboagye

Open Access Theses & Dissertations

In this work, we present an application of Stochastic Control Theory to the Merton's portfolio optimization problem. Then, the dynamic programming methodology is applied to reduce the whole problem to solving the well-known HJB (Hamilton-Jacobi-Bellman) equation that arises from the Merton's portfolio optimization problem subject to the power utility function. Finally, a numerical method is proposed to solve the HJB equation and the optimal strategy. The numerical solutions are compared with the explicit solutions for optimal consumption and investment control policies.

Mathematical Modeling Of Tumor Growth For Free-Boundary Problem By Enhanced Finite Volume Method, Mashriq Ahmed Saleh

Open Access Theses & Dissertations

Modeling tumor growth due to infiltration of immune cells presents several challenges in numerical computations. First, it involves multiple cell species whose total number should be a constant, due to the incompressibility assumption; second, by mapping the Eulerian coordinate of the free-boundary problem onto a fixed logical domain, geometric source terms appear and they need to be addressed properly in numerical methods. In this work, we use a simplified model that contains two species and prescribed infiltration velocity and to show that the conventional finite volume methods fail to preserve the trivial (constant) solutions. To this end, we introduce the …

Integrated Statistical And Machine Learning Algorithms For Predicting And Classifying G Protein-Coupled Receptors, Fredrick Ayivor

Open Access Theses & Dissertations

G protein-coupled receptors (GPCRs) are transmembrane proteins with important functions in signal transduction and often serve as drug targets. With increasing availability of protein sequence information, there is much interest in computationally predicting GPCRs and classifying them according to their biological roles. Such predictions are cost-efficient and can be valuable guides for designing wet lab experiments to help elucidate signaling pathways and expedite drug discovery. There are existing computational tools of GPCR prediction that involve principal component analysis (PCA), intimate sorting (IS), support vector machine, and random forest (RF) techniques using various sequence derived features. While accuracies of over 90\% …

A Mixed Finite Element Method For The Coupling Of Linear Elasticity And Stokes Flow, Maranda Bean

Open Access Theses & Dissertations

The complex interaction between fluids and structures require the coupling the laws concerning structure mechanics and fluid dynamics and are of vital importance to many scientific and engineering fields. We propose a method for modeling the coupling of a linearly elastic solid and slow fluid flow modeled by Stokes equations. The model equations are expressed in terms of displacement, velocity and stress. With these primary variables, we use a single mixed finite element space based on the Hellinger-Reissner variational principle for linear elasticity to discretize the resulting system spatially. This results in more accurate approximations for stress than those obtained …

On The Spatial Modelling Of Mixed And Constrained Geospatial Data, Hassan Talebi

Theses: Doctorates and Masters

Spatial uncertainty modelling and prediction of a set of regionalized dependent variables from various sample spaces (e.g. continuous and categorical) is a common challenge for geoscience modellers and many geoscience applications such as evaluation of mineral resources, characterization of oil reservoirs or hydrology of groundwater. To consider the complex statistical and spatial relationships, categorical data such as rock types, soil types, alteration units, and continental crustal blocks should be modelled jointly with other continuous attributes (e.g. porosity, permeability, seismic velocity, mineral and geochemical compositions or pollutant concentration). These multivariate geospatial data normally have complex statistical and spatial relationships which should …

Menstrual Cycle And The Temporal Discrimination Threshold, Eavan M. Mc Govern, Emer O'Connor, Ines Beiser, Laura Williams, John Butler, Brendan Quinlivan, Shruti Narasimham, Rebecca Beck, Richard B. Reilly, Sean O'Riordan, Michael Hutchinson

Articles

The temporal discrimination threshold (TDT) is a proposed pre-clinical biomarker (endophenotype) for adult onset isolated focal dystonia (AOIFD). Age- and sex-related effects on temporal discrimination demonstrate that women, before the age of 40 years, have faster temporal discrimination than men but their TDTs worsen with age at almost three times the rate of men. Thus after 40 years the TDT in women is progressively worse than in men. AOIFD is an increasingly female-predominant disorder after the age of 40; it is not clear whether this age-related sexually-dimorphic difference observed for both the TDT and sex ratio at disease onset in …

Cognitive Load Reduces The Effects Of Optic Flow On Gait And 2 Electrocortical Dynamics During Treadmill Walking 3, Brenda Malcolm, John J. Foxe, John Butler, Sophie Molholm, Pierfilippo De Sanctis

Articles

While navigating complex environments the brain must continuously adapt to both external demands such as fluctuating sensory inputs, as well as internal demands, such as engagement in a cognitively demanding task. Previous studies have demonstrated changes in behavior and gait with increased sensory and cognitive load, but the underlying cortical mechanisms remain largely unknown. Here, in a Mobile Brain/Body Imaging (MoBI) approach sixteen young adults walked on a treadmill with high-density EEG while 3D motion capture tracked kinematics of the head and feet. Visual load was manipulated with the presentation of optic flow with and without continuous mediolateral perturbations. The …

Penerapan Matriks Leslie Pada Angka Kelahiran Dan Harapan Hidup Wanita Di Provinsi Jawa Timur, Dewi Anggreini, Ratri Candra Hastari

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Tujuan penelitian ini adalah menentukan banyaknya populasi wanita di Provinsi Jawa Timur berdasarkan angka kelahiran dan harapan hidup menggunakan nilai eigen dan vektor eigen serta untuk mengetahui distribusi umur pembatas menggunakan model matriks Leslie. Vektor eigen digunakan untuk menentukan banyaknya populasi wanita dari masing-masing interval umur, sedangkan nilai eigen digunakan untuk menentukan laju pertumbuhan penduduk. Metode penelitian yang digunakan pada Tahap pertama adalah menentukan subjek penelitian dan Tahap Kedua adalah (a) mengumpulkan data penelitian (b) analisis data dan terakhir menarik kesimpulan. Data penelitian ini diperoleh dari BPS Provinsi Jawa Timur yaitu jumlah penduduk wanita dari tahun 2010-2015. Hasil penelitian ini …

Latent Root Regression Dalam Mengatasi Multikolinearitas, Desy Pramesti Untari, Mathilda Susanti

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Salah satu metode yang dapat digunakan untuk mengatasi masalah multikolinearitas pada model regresi adalah latent root regression. Latent root regression merupakan perluasan dari principal component regression. Tujuan penelitian ini adalah untuk melakukan analisis latent root regression dalam mengatasi multikolinearitas yang diterapkan pada faktor-faktor yang mempengaruhi IHSG di Bursa Efek Indonesia. Variabel-variabel yang digunakan pada penelitian ini adalah IHSG, jumlah uang beredar, kurs rupiah terhadap dolar AS, harga emas dunia dan Indeks Dow Jones. Hasil penelitian yang diperoleh adalah faktor jumlah uang beredar, kurs rupiah terhadap dolar AS, harga emas dunia dan Indeks Dow Jones berpengaruh terhadap IHSG, namun …

Penerapan Skema Tanda Tangan Schnorr Pada Pembuatan Tanda Tangan Digital, Herdita Fajar Isnaini, Karyati Karyati

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Tanda tangan digital dapat dijadikan sebagai salah satu cara untuk menjamin keaslian pesan atau informasi yang diterima. Salah satu skema yang dapat digunakan dalam membentuk tanda tangan adalah skema tanda tangan Schnorr. Skema tanda tangan ini berdasarkan pada masalah logaritma diskret. Skema ini memerlukan penggunaan fungsi hash yang akan menghasilkan nilai hash pesan untuk pembuatan tanda tangan, yang menjadi salah satu alasan keamanan dari skema ini. Skema tanda tangan Schnorr terdiri dari tiga proses, yaitu: pembentukan kunci, pembuatan tanda tangan serta verifikasi. Kajian ini akan membahas mengenai skema tanda tangan Schnorr dalam membentuk tanda tangan digital sebagai pengaman keaslian …

Numerical Methods And Simulation For Time Dependent Electrokinetic Flow, Rui Cao

Dissertations

Electrokinetic flow typically occurs when an electric field is applied to a fluid electrolyte in the presence of a boundary or interface. The electric field induces a force that causes oppositely charged ions to migrate in opposite directions while simultaneously diffusing due to Brownian motion. In an unbounded medium this process, which is called electrodiffusion, does not separate bulk electric charge into separate regions and causes no bulk motion of the host fluid solvent. However, in the presence of a boundary or interface that either impedes or is impervious to the movement of ions in the normal direction, the normal …

Expression Of Wnt-Signaling Pathway Genes And Their Associations With Mirnas In Colorectal Cancer, Martha L. Slattery, Lila E. Mullany, Lori C. Sakoda, Wade S. Samowitz, Roger K. Wolff, John R. Stevens, Jennifer S. Herrick

Mathematics and Statistics Faculty Publications

The Wnt-signaling pathway functions in regulating cell growth and thus is involved in the carcinogenic process of several cancers, including colorectal cancer. We tested the hypothesis that multiple genes in this signaling pathway are dysregulated and that miRNAs are associated with these dysregulated genes. We used data from 217 colorectal cancer (CRC) cases to evaluate differences in Wnt-signaling pathway gene expression between paired CRC and normal mucosa and identify miRNAs that are associated with these genes. Gene expression data from RNA-Seq and miRNA expression data from Agilent Human miRNA Microarray V19.0 were analyzed. We focused on genes most strongly associated …

Reconstructing Results From Voting Theory Using Linear Algebra, Brian Camara

Honors Program Theses and Projects

For many undergraduate students, achieving an understanding of upper-level mathematics can be extremely challenging. For us, it helps to connect these new concepts with material we are familiar with. This will be the central theme of this thesis. We will introduce some basic components of algebraic voting theory, along with briey discussing how (Daugherty, Eustis, Minton, & Orrison, 2009) used representation theory to achieve their results. We will then provide an alternative proof to the main result of the (Daugherty et al., 2009) article using linear algebra, which should be much more familiar to my peers. We will carry out …

Weighted Inequalities For Dyadic Operators Over Spaces Of Homogeneous Type, David Edward Weirich

Mathematics & Statistics ETDs

A so-called space of homogeneous type is a set equipped with a quasi-metric and a doubling measure. We give a survey of results spanning the last few decades concerning the geometric properties of such spaces, culminating in the description of a system of dyadic cubes in this setting whose properties mirror the more familiar dyadic lattices in R^n . We then use these cubes to prove a result pertaining to weighted inequality theory over such spaces. We develop a general method for extending Bellman function type arguments from the real line to spaces of homogeneous type. Finally, we uses this …

Discovering And Demonstrating Patterns, Maria Klawe

The Transdisciplinary STEAM+ Journal

Harvey Mudd College's President Maria Klawe shares her personal journey in combining a love of mathematics and art.

New Implementations For Tabulating Pseudoprimes And Liars, Wuyang Liu

Honors Projects

Whether it is applied to primality test or cryptography, pseudoprimes are one of the most important topics in number theory. Regarding the study of strong pseudoprimes, there are two problems which mathematicians have been working on:
1. Given a, b, find all a-spsp up to b.
2. Given an odd composite n, find all a -n such that n is an a-spsp.
where n = a-spsp means n is a strong pseudoprime to base a, and a is a strong liar of n.

The two problems are respectively referred to as …

Can Addressing Language Skills For Fifth Grade Ells In A Multiplication Curriculum Help Address The Achievement Gap In Math? A Multiplication Workbook For Big Kids, Michelle Douglas

Master's Projects and Capstones

Currently, the state of California has 1,332,405 students from grades k-12 who speak a language other than English at home (Caledfacts, 2016). When I started my first year teaching fifth grade with 95% of my students being English language learners (ELLs), I was surprised to see an achievement gap of two to three years in my student’s reading and math skills. I found that my student’s developmental language and math skills contributed to a lack of engagement during math time. Upon further research, I found that these three factors play a role in the wide achievement gaps between ELLs and …

Hodge Theory On Transversely Symplectic Foliations, Yi Lin

Mathematical Sciences: Faculty Publications

In this paper, we develop symplectic Hodge theory on transversely symplectic foliations. In particular, we establish the symplectic dδ-lemma for any such foliations with the (transverse) s-Lefschetz property. As transversely symplectic foliations include many geometric structures, such as contact manifolds, co-symplectic manifolds, symplectic orbifolds, and symplectic quasi-folds as special examples, our work provides a unifying treatment of symplectic Hodge theory in these geometries.

As an application, we show that on compact K-contact manifolds, the s-Lefschetz property implies a general result on the vanishing of cup products, and that the cup length of a 2n+1 dimensional compact K-contact manifold with the …

Characterizations Of Some Classes Of Graphs That Are Nearly Series-Parallel, Victoria Fontaine

LSU Doctoral Dissertations

A series-parallel graph can be built from a single-edge graph by a sequence of series and parallel extensions. The class of such graphs coincides with the class of graphs that do not have the complete graph K₄ as a minor. This dissertation considers a class M₁ of graphs that are close to being series-parallel. In particular, every member of the class has the property that one can obtain a series-parallel graph by adding a new edge and contracting it out, or by splitting a vertex into two vertices whose neighbor sets partition the neighbor set of the original …