Mathematics Commons^™

Imprecise Probabilities In Engineering Analyses, Michael Beer, Scott Ferson, Vladik Kreinovich

Departmental Technical Reports (CS)

Probabilistic uncertainty and imprecision in structural parameters and in environmental conditions and loads are challenging phenomena in engineering analyses. They require appropriate mathematical modeling and quantification to obtain realistic results when predicting the behavior and reliability of engineering structures and systems. But the modeling and quantification is complicated by the characteristics of the available information, which involves, for example, sparse data, poor measurements and subjective information. This raises the question whether the available information is sufficient for probabilistic modeling or rather suggests a set-theoretical approach. The framework of imprecise probabilities provides a mathematical basis to deal with these problems which …

Spock, Euler, And Madison: Graph Theory In The Classroom, Michael Buhler

Undergraduate Honors Capstone Projects

This work is an attempt to accomplish two main objectives. First is to encourage secondary students to engage in the kinds of mathematical reasoning skills that will be necessary to them when they move to college math classes. My experience in college, along with that of many others is that "school math," with its obsession with calculations and memorization, is dreadfully insufficient in preparing students for the proof and reasoning-based classes they will face in high school. This is an attempt to integrate some of those reasoning skills into high school courses using graph theory as a vehicle.

The second …

The Use Of Statistics In Experimental Physics, Thomas J. Pfaff, Maksim Sipos, M. C. Sullivan, B. G. Thompson, Max Tran

Publications and Research

Most mathematicians are aware of the importance of statistics in biological sciences, business, and economics, but are less aware that statistics is used every day in experimental physics. This paper gives three interesting examples of how statistics plays a vital role in physics. These examples use the basic statistical tools of residuals analysis and goodness of fit.

Measuring A Circle: A Math Lesson For Grades 5-10, Robert C. Moore

Faculty Publications

This article is designed to promote teaching methods that engage students in active learning and result in deep conceptual understanding by offering a sample lesson to help students (grades 5-10, ages 10-15) answer questions about and gain a deeper understanding of how to measure the circumference and area of a circle.

Student Centered Mathematics In An Isolated Skill Environment-Constructivist Methods In Mathematics, Amy Katherine Sorenson

Mathematics Graduate Theses

"A research paper submitted to the Faculty of the Department of Mathematics in partial fulfillment of the requirements for the degree of Master of Science in Elementary and Middle Mathematics Education"

Improving Student Achievement Through Feedback, Jennifer L. Mchlachlan

Mathematics Graduate Theses

This paper reviews the current research that exists on feedback given to students in an educational setting. Questions examined were what characteristics make feedback effective, what are the effects on student achievement if feedback is available to students in a math classroom and does timing of the feedback given play a role in its effectiveness. Results showed that feedback is effective if it is descriptive, including both strengths and weaknesses. Feedback given in small doses throughout the learning process, so as not to overwhelm students, has also proven effective. The research shows that the effect of feedback on student achievement …

Volume 05, Ian Karamarkovich, Jessica Cox, Kyle Fowlkes, Allison Pawlowski, Kaitlin Major, Carrie Dunham, Kelsey Scheitlin, Kathryn Grayson, Ashley Johnson, Jennifer Nehrt, Kelsey Stolzenbach, Kristin Mcquarrie, Sara Nelson, Melisa Michelle, Jessica Sudlow, Perry Bason, Danielle Dmuchawski, Mariah Asbell, Matthew Sakach, Timothy Smith Jr., Annaliese Troxell, T. Dane Summerell, Sarah Ganrude, Malina Rutherford, Hannah Hopper, John Berry Jr., James Early, Colleen Festa, Chelsea D. Taylor, Michelle Maddox, Kaitlyn Smith, Sarah Schu, Cabell Edmunds, Katherine Grayson, Kayla Tornai

Incite: The Journal of Undergraduate Scholarship

Introduction from Dean Dr. Charles Ross

The Tallis House as an Extension of Emily Tallis in McEwan's Atonement by Ian Karamarkovich

Graphic Design by Jessica Cox

Graphic Design by Kyle Fowlkes

Graphic Design by Allison Pawlowski

Incorporating Original Research in The Classroom: A Case Study Analyzing the Influence of the Chesapeake Bay on Local Temperatures by Kaitlin Major, Carrie Dunham and Dr. Kelsey Scheitlin

Graphic Design by Kathryn Grayson

Graphic Design by Ashley Johnson

Facing the Music: Environmental Impact Assessment of Building A Concert Hall on North Campus by Jennifer Nehrt, Kelsey Stolzenbach And Dr. Kelsey Scheitlin

Art by Kristin …

Combinatorial Pooling Enables Selective Sequencing Of The Barley Gene Space, Stefano Lonardi, Denisa Duma, Matthew Alpert, Francesca Cordero, Marco Beccuti, Prasanna R. Bhat, Yonghui Wu, Gianfranco Ciardo, Burair Alsaihati, Steve Wanamaker, Josh Resnik, Serdar Bozdag, Ming-Cheng Luo, Timothy J. Close

Mathematics, Statistics and Computer Science Faculty Research and Publications

For the vast majority of species – including many economically or ecologically important organisms, progress in biological research is hampered due to the lack of a reference genome sequence. Despite recent advances in sequencing technologies, several factors still limit the availability of such a critical resource. At the same time, many research groups and international consortia have already produced BAC libraries and physical maps and now are in a position to proceed with the development of whole-genome sequences organized around a physical map anchored to a genetic map. We propose a BAC-by-BAC sequencing protocol that combines combinatorial pooling design and …

Weighted Shifts Of Finite Multiplicity, Daniel S. Sievewright

Dissertations

We will discuss the structure of weighted shift operators on a separable, infinite dimensional, complex Hilbert space. A weighted shift is said to have multiplicity n when all the weights are n x n matrices. To study these weighted shifts, we will investigate which operators can belong to the Deddens algebras and spectral radius algebras, which can be quite large. This will lead to the necessary and sufficient conditions for these algebras to have a nontrivial invariant subspace.

Direct Eit Reconstructions Of Complex Admittivities On A Chest-Shaped Domain In 2-D, Sarah J. Hamilton, Jennifer L. Mueller

Mathematics, Statistics and Computer Science Faculty Research and Publications

Electrical impedance tomography (EIT) is a medical imaging technique in which current is applied on electrodes on the surface of the body, the resulting voltage is measured, and an inverse problem is solved to recover the conductivity and/or permittivity in the interior. Images are then formed from the reconstructed conductivity and permittivity distributions. In the 2-D geometry, EIT is clinically useful for chest imaging. In this work, an implementation of a D-bar method for complex admittivities on a general 2-D domain is presented. In particular, reconstructions are computed on a chest-shaped domain for several realistic phantoms including a simulated pneumothorax, …

Age-Specific Signatures Of Glioblastoma At The Genomic, Genetic, And Epigenetic Levels, Serdar Bozdag, Aiguo Li, Gregory Riddick, Yuri Kotliarov, Mehmet Baysan, Fabio M. Iwamoto, Margaret C. Cam, Svetlana Kotliarova, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Age is a powerful predictor of survival in glioblastoma multiforme (GBM) yet the biological basis for the difference in clinical outcome is mostly unknown. Discovering genes and pathways that would explain age-specific survival difference could generate opportunities for novel therapeutics for GBM. Here we have integrated gene expression, exon expression, microRNA expression, copy number alteration, SNP, whole exome sequence, and DNA methylation data sets of a cohort of GBM patients in The Cancer Genome Atlas (TCGA) project to discover age-specific signatures at the transcriptional, genetic, and epigenetic levels and validated our findings on the REMBRANDT data set. We found major …

Repeated Changes In Reported Sexual Orientation Identity Linked To Substance Use Behaviors In Youth, Miles Q. Ott, David Wypij, Heather L. Corliss, Margaret Rosario, Sari L. Reisner, Allegra R. Gordon, S. Bryn Austin

Statistical and Data Sciences: Faculty Publications

Purpose—Previous studies have found that sexual minority (e.g., lesbian, gay, bisexual) adolescents are at higher risk of substance use than heterosexuals, but few have examined how changes in sexual orientation over time may relate to substance use. We examined the associations between change in sexual orientation identity and marijuana use, tobacco use, and binge drinking in U.S. youth.

Methods—Prospective data from 10,515 U.S. youth ages 12-27 years in a longitudinal cohort study were analyzed using sexual orientation identity mobility measure M (frequency of change from 0 [no change] to 1 [change at every wave]) in up to five waves of …

2013 (Spring), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2013 Spring Colloquium.

Diminished Antioxidant Activity Of High-Density Lipoprotein–Associated Proteins In Chronic Kidney Disease, David J. Kennedy, W.H. Wilson Tang, Yiying Fan, Yuping Wu, Shirley Mann, Michael Pepoy, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Background:Decreased serum arylesterase activity, catalyzed by the high-density lipoprotein–associated paraoxonase (PON)-1, is associated with increased oxidant stress and atherosclerosis risk. We sought to determine the prognostic value of serum PON-1 activity, as monitored by PON or arylesterase activities, in subjects with chronic kidney disease (CKD), particularly in relation to established cardiac biomarkers.Methods and Results: Serum arylesterase and PON activities were measured in sequential subjects with CKD (n=630; estimated glomerular filtration rate [eGFR] <60 mL/min per 1.73 m2) and an age- and sex-matched control group of non-CKD subjects (n=315) presenting for cardiac evaluations and prospectively followed for incident (3-year) major adverse cardiac events (composite of death, nonfatal myocardial infarction, and stroke). Serum arylesterase activity in CKD subjects was lower compared with that in non-CKD control subjects [median (interquartile range) 94 (77 to 112) versus 103 (85 to 121) μmol(L·min) per mL, P<0.001]; similarly, PON activity in CKD subjects was lower compared with that in non-CKD control subjects [median (interquartile range) 474 (275 to 936) versus 586 (301 to 1118) nmol(L·min) per mL, P<0.001]. Lower serum arylesterase (hazard ratio 1.8, 95% CI 1.26 to 2.57, P<0.01) was a predictor of poorer outcomes. After adjusting for traditional risk factors and medication use, lower serum arylesterase (hazard ratio 1.55, 95% CI 1.08 to 2.23, P<0.05) still conferred an increased risk of major adverse cardiac events at 3 years. Conclusions: In patients with CKD, decreased serum arylesterase activity, a measure of diminished antioxidant properties of PON-1, predicts higher risk of incident long-term adverse cardiovascular events (heart attack, stroke, or death) in multivariable models adjusting for established clinical and biochemical risk factors.

Variational Methods On Elastic Curves, Daniel D. Rocker

College of Graduate Studies: Theses & Dissertations

In this thesis we investigate elastic curves. These are curves with minimal bending energy as measured by the total squared curvature functional. We show that these can be computed by evolving curves in the direction of the negative gradient in certain Hilbert space settings. By discretizing the curves and using numerical integration, we compute approximate minimizers and display using computer graphics. We propose a conjecture based on the rotation number of a curve that predicts the critical point curves that minimize bending energy.

Approximate Similarity Reduction, Rui Zhang

College of Graduate Studies: Theses & Dissertations

The nonlinear K (n;1) equation with damping is investigated via the approximate homotopy symmetry method and approximate homotopy direct method. The approximate homotopy symmetry and homotopy similarity reduction equations of different orders are derived and the corresponding homotopy series reduction solutionsare obtained. As a result, the formal coincidence for both methods is displayed.

The String Landscape: On Formulas For Counting Vacua, Tamar Friedmann, Richard P. Stanley

Mathematics Sciences: Faculty Publications

We derive formulas for counting certain classes of vacua in the string/M theory landscape. We do so in the context of the moduli space of M-theory compactifications on singular manifolds with G₂ holonomy. Particularly, we count the numbers of gauge theories with different gauge groups but equal numbers of U (1) factors which are dual to each other. The vacua correspond to various symmetry breaking patterns of grand unified theories. Counting these dual vacua is equivalent to counting the number of conjugacy classes of elements of finite order inside Lie groups. We also point out certain cases where the …

Statistical Properties Of The Mc-Dagum And Related Distributions, Sasith Rajasooriya

College of Graduate Studies: Theses & Dissertations

In this thesis, we present a new class of distributions called Mc-Dagum distribution. This class of distributions contains several distributions such as beta-Dagum, beta-Burr III, beta-Fisk and Dagum distributions as special cases. The hazard function, reverse hazard function, moments and mean residual life function are obtained. Inequality measures, entropy and Fisher information are presented. Maximum likelihood estimates of the model parameters are given.

Difference Sets In Non-Abelian Groups Of Order 256, Taylor Applebaum

Honors Theses

This paper considers the problem of determining which of the 56092 groups of order 256 contain (256; 120; 56; 64) difference sets. John Dillon at the National Security Agency communicated 724 groups which were still open as of August 2012. In this paper, we present a construction method for groups containing a normal subgroup isomorphic to Z4 Z4 Z2 . This construction method was able to produce difference sets in 643 of the 649 unsolved groups with the correct normal subgroup. These constructions elimated approximately 90% of the open cases, leaving 81 remaining unsolved groups.

Power Distribution In The European Union, Dayton Steele

Honors Theses

The Treaty of Lisbon, the latest treaty governing law-making in the European Union (EU), was ratified in 2009 and goes fully into effect in 2014. This treaty, with its change to voting procedures in the Council of Ministers, claims to make decision-making in the EU more democratic and more efficient. Since the EU serves as an economic and political entity, we will assess these claims by comparing each member state's GDP and population to its power as modeled using the concept of a power index from the game theory literature. We will utilize the normalized Banzhaf index, the Shapley-Shubik index, …