Physical Sciences and Mathematics Commons^™

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 …

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 …

Learning About Modeling In Teacher Preparation Programs, Hyunyi Jung, Eryn Stehr, Jia He, Sharon L. Senk

Hyunyi Jung

This study explores opportunities that secondary mathematics teacher preparation programs provide to learn about modeling in algebra. Forty-eight course instructors and ten focus groups at five universities were interviewed to answer questions related to modeling. With the analysis of the interview transcripts and related course materials, we found few opportunities for PSTs to engage with the full modeling cycle. Examples of opportunities to learn about algebraic modeling and the participants’ perspectives on the opportunities can contribute to the study of modeling and algebra in teacher education.

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 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

Department of 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 …

Experimenting With The Identity (Xy)Z = Y(Zx), Irvin Roy Hentzel, David P. Jacobs, Sekhar V. Muddana

Irvin Roy Hentzel

An experiment with the nonassociative algebra program Albert led to the discovery of the following surprising theorem. Let G be a groupoid satisfying the identity (xy)z = y(zx). Then for products in G involving at least five elements, all factors commute and associate. A corollary is that any semiprime ring satisfying this identity must be commutative and associative, generalizing a known result of Chen.

Semiprime Locally(-1, 1) Ring With Minimal Condition, Irvin R. Hentzel, H. F. Smith

Irvin Roy Hentzel

Let L be a left ideal of a right alternative ring A with characteristic ::/=2. If L is maximal and nil, then L is a two-sided ideal. If L is minimal, then it is either a two-sided ideal, or the ideal it generates is contained in the right nucleus of A. In particular, if A is prime, then a minimal left ideal of A must be a two-sided ideal. Let A be a semiprime locally (-1, 1) ring with characteristic ::1=2, 3. Then A is isomorphic to a subdirect sum of an alternative ring, a strong (-1, 1) ring, and …

Minimal Identities Of Bernstein Alegebras, Irvin R. Hentzel, Ivan Correa, Luiz Antionio Peresi

Irvin Roy Hentzel

We construct the minimal identities for Bernstein algebras, exceptional Bernstein algebras and normal Bernstein algebras. We use the technique of processing identities via the representation of the symmetric groups. The computer algorithms for creating the standard tableaus and the integral representations are summarized.

Counterexamples In Nonassociative Algebra, Irvin R. Hentzel, Luiz Antonio Peresi

Irvin Roy Hentzel

We present a method of constructing counterexamples in nonassociative algebra. The heart of the computation is constructing a matrix of identities and reducing this matrix (usually very sparse) to row canonical form. The example is constructed from the entries in one column of this row canonical form. While this procedure is not polynomial in the degree of the identity, several shortcuts are listed which shorten calculations. Several examples are given.

On Preserving Structured Matrices Using Double Bracket Operators: Tridiagonal And Toeplitz Matrices, Kenneth Driessel, Irvin R. Hentzel, Wasin So

Irvin Roy Hentzel

In the algebra of square matrices over the complex numbers, denotes Two problems are solved: (1) Find all Hermitian matrices M which have the following property: For every Hermitian matrix A, if A is tridiagonal, then so is (2) Find all Hermitian matrices M which have the following property: For every Hermitian matrix A, if A is Toeplitz, then so is

On Prime Right Alternative Algebras And Alternators, Giulia Maria Piacentini Cattaneo, Irvin R. Hentzel

Irvin Roy Hentzel

We study subvarieties of the variety of right alternative algebras over a field of characteristic t2,t3 such that the defining identities of the variety force the span of the alternators to be an ideal and do not force an algebra with identity element to be alternative. We call a member of such a variety a right alternative alternator ideal algebra. We characterize the algebras of this subvariety by finding an identity which holds if and only if an algebra belongs to the subvariety. We use this identity to prove that if R is a prime, right alternative alternator ideal algebra …

Using Mixed Effects Modeling To Quantify Difference Between Patient Groups With Diabetic Foot Ulcers, Rachel French

Mahurin Honors College Capstone Experience/Thesis Projects

When diabetes progresses, many patients suffer from chronic foot ulcers. In a study described in Matrix Metalloproteinases and Diabetic Foot Ulcers (Muller et al., 2008), sixteen patients with diabetic foot ulcers were examined throughout a twelve week healing period. During this period, levels of matrix metalloproteinases (MMP-1), their inhibitors (TIMP-1), and the extracellular matrix in a wound area were measured at distinct time intervals for each patient. The ratios of these healing components are vital in determining whether a wound will heal or become chronic and never properly heal. Connecting Local and Global Sensitivities in a Mathematical Model for Wound …

Improving The Problem With Problem Solving, Cole Thibert

Essential Studies UNDergraduate Showcase

As a prospective math educator who will be teaching in the near future, I was concerned with the idea of preparing my future students for college math courses. I decided to research the effects of teaching students how to appropriately use problem solving strategies in math. My research led me towards looking at the benefits of students becoming better problem solvers and how teachers can implement problem solving into their daily lessons.

When this implementation is successful, students can become more independent with their learning, they are able to work and persevere through challenging problems, and they have a greater …

Gödel’S Incompleteness Theorem, Emma Buntrock

Essential Studies UNDergraduate Showcase

In 1931 Gödel released his Incompleteness Theorem. His theorem was the opposite of what other mathematicians at the time wanted, but it was very influential to realize there is no perfectly complete formal systems. The incompleteness theorem is based of the idea that in a consistent system there are pieces that can not be proved or disproved, causing for incompleteness. The second part of that idea is that such a system can not prove that itself is consistent, which also makes it incomplete. I will verify theses proofs using a series of logic problems that show how a system is …

The Most Important Statistics In Football, Jacob Holmen

Essential Studies UNDergraduate Showcase

This research is based on the Five Factors that were devised by Bill Connelly of SBNation. The Five Factors of football include Explosiveness, Efficiency, Field Position, Finishing Drives, and Turnovers. Each factor is composed of associated statistics that when put together make up the most important statistics in football. This research includes the analysis of all 857 FBS (the highest level of NCAA Division I football) games from the 2016 season. Data was analyzed through the use of an Excel spreadsheet. Five different statistics were looked at, each associated with one of the Five Factors. The statistics include Yards per …

Analytics And Baseball's New Generation, John Roche

Essential Studies UNDergraduate Showcase

Major League Baseball has been a catalyst for making decisions in sports and competition from a purely mathematical viewpoint. We have seen teams utilize unique on-field player alignments and roster-building strategies based on statistical observations and applications of math. This project examines the advantages Sabermetrics and analytics present within the sport. Untapped statistical categories that could further the success of teams in the future is also briefly discussed.

Statistical Analysis Of Momentum In Basketball, Mackenzi Stump

Honors Projects

The “hot hand” in sports has been debated for as long as sports have been around. The debate involves whether streaks and slumps in sports are true phenomena or just simply perceptions in the mind of the human viewer. This statistical analysis of momentum in basketball analyzes the distribution of time between scoring events for the BGSU Women’s Basketball team from 2011-2017. We discuss how the distribution of time between scoring events changes with normal game factors such as location of the game, game outcome, and several other factors. If scoring events during a game were always randomly distributed, or …

The Calculus War: The Ultimate Clash Of Genius, Walker Briles Bussey-Spencer

Chancellor’s Honors Program Projects

No abstract provided.

Optimal Layout For A Component Grid, Michael W. Ebert

Computer Science and Software Engineering

Several puzzle games include a specific type of optimization problem: given components that produce and consume different resources and a grid of squares, find the optimal way to place the components to maximize output. I developed a method to evaluate potential solutions quickly and automated the solving of the problem using a genetic algorithm.

Degree And Neighborhood Conditions For Hamiltonicity Of Claw-Free Graphs, Zhi-Hong Chen

Scholarship and Professional Work - LAS

For a graph H , let σ t ( H ) = min { Σ i = 1 t d H ( v i ) | { v 1 , v 2 , … , v t } is an independent set in H } and let U t ( H ) = min { | ⋃ i = 1 t N H ( v i ) | | { v 1 , v 2 , ⋯ , v t } is an independent set in H } . We show that for a given number ϵ and given integers …

Introduction To The Usu Library Of Solutions To The Einstein Field Equations, Ian M. Anderson, Charles G. Torre

Tutorials on... in 1 hour or less

This is a Maple worksheet providing an introduction to the USU Library of Solutions to the Einstein Field Equations. The library is part of the DifferentialGeometry software project and is a collection of symbolic data and metadata describing solutions to the Einstein equations.

Quantum Econometrics: How To Explain Its Quantitative Successes And How The Resulting Formulas Are Related To Scale Invariance, Entropy, Fuzzy, And Copulas, Hung T. Nguyen, Kittawit Autchariyapanitkul, Olga Kosheleva, Vladik Kreinovich, Songsak Sriboonchitta

Departmental Technical Reports (CS)

Many aspects of human behavior seem to be well-described by formulas of quantum physics. In this paper, we explain this phenomenon by showing that the corresponding quantum-looking formulas can be derived from the general ideas of scale invariance, fuzziness, and copulas. We also use these ideas to derive a general family of formulas that include non-quantum and quantum probabilities as particular cases -- formulas that may be more adequate for describing human behavior than purely non-quantum or purely quantum ones.

Why Rectified Linear Neurons Are Efficient: Symmetry-Based, Complexity-Based, And Fuzzy-Based Explanations, Olac Fuentes, Justin Parra, Elizabeth Y. Anthony, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditionally, neural networks used a sigmoid activation function. Recently, it turned out that piecewise linear activation functions are much more efficient -- especially in deep learning applications. However, so far, there have been no convincing theoretical explanation for this empirical efficiency. In this paper, we show that, by using different uncertainty techniques, we can come up with several explanations for the efficiency of piecewise linear neural networks. The existence of several different explanations makes us even more confident in our results -- and thus, in the efficiency of piecewise linear activation functions.