Mathematics Commons^™

Statistical Modeling Of Earthquake Damage, Allison Nicole Waters

Honors Program Theses

The purpose of this study was to build a statistical model of the economic damage that arises from earthquakes in order to better predict losses from future earthquakes. Though earthquakes are essentially a random event and cannot be fully anticipated, analyzing historical data and creating a statistical model can provide researchers with a more accurate estimate of future losses. The data set from which this model was built incorporated earthquakes occurring worldwide from 1915-2015 in which the total damage was recorded. The final model was a multiple linear regression model explaining total damage resulting from an earthquake through four independent …

Further Results On Edge - Odd Graceful Graphs, Mohammed Seoud, Maher Salim

Turkish Journal of Mathematics

wheel $W_n$, for $n\equiv 1,\ 2$ and $3\ mod\ 4$; $C_n\bigodot\bar{K}_{2m-1}$; even helms; $P_n\bigodot\bar{K}_{2m}$ and $K_{2,s}$. Also we present two theorems of non edge - odd graceful graphs and an idea to label complete graphs.

Realizing The 2-Associahedron, Patrick N. Tierney

HMC Senior Theses

The associahedron has appeared in numerous contexts throughout the field of mathematics. By representing the associahedron as a poset of tubings, Michael Carr and Satyan L. Devadoss were able to create a gener- alized version of the associahedron in the graph-associahedron. We seek to create an alternative generalization of the associahedron by considering a particle-collision model. By extending this model to what we dub the 2- associahedron, we seek to further understand the space of generalizations of the associahedron.

Interval Graphs, Joyce C. Yang

HMC Senior Theses

We examine the problem of counting interval graphs. We answer the question posed by Hanlon, of whether the formal power series generating function of the number of interval graphs on n vertices has a positive radius of convergence. We have found that it is zero. We have obtained a lower bound and an upper bound on the number of interval graphs on n vertices. We also study the application of interval graphs to the dynamic storage allocation problem. Dynamic storage allocation has been shown to be NP-complete by Stockmeyer. Coloring interval graphs on-line has applications to dynamic storage allocation. The …

To The Memory Of R. Freivalds, Efim Kinber

School of Computer Science & Engineering Faculty Publications

The paper contains author’s memories of his mentor and teacher R. M. Freivalds.

The Bourgain Spaces And Recovery Of Magnetic And Electric Potentials Of Schrödinger Operators, Yaowei Zhang

Theses and Dissertations--Mathematics

We consider the inverse problem for the magnetic Schrödinger operator with the assumption that the magnetic potential is in C^λ and the electric potential is of the form p₁ + div p₂ with p₁, p₂ ∈ C^λ. We use semiclassical pseudodifferential operators on semiclassical Sobolev spaces and Bourgain type spaces. The Bourgain type spaces are defined using the symbol of the operator h²Δ + hμ ⋅ D. Our main result gives a procedure for recovering the curl of the magnetic field and the electric potential from the Dirichlet to Neumann …

Efficient Image Processing Via Compressive Sensing Of Integrate-And-Fire Neuronal Network Dynamics, Victor J. Barranca, G. Kovačič, D. Zhou, D. Cai

Mathematics & Statistics Faculty Works

Integrate-and-fire (I&F) neuronal networks are ubiquitous in diverse image processing applications, including image segmentation and visual perception. While conventional I&F network image processing requires the number of nodes composing the network to be equal to the number of image pixels driving the network, we determine whether I&F dynamics can accurately transmit image information when there are significantly fewer nodes than network input-signal components. Although compressive sensing (CS) theory facilitates the recovery of images using very few samples through linear signal processing, it does not address whether similar signal recovery techniques facilitate reconstructions through measurement of the nonlinear dynamics of an …

Choline Diet And Its Gut Microbe–Derived Metabolite, Trimethylamine N-Oxide, Exacerbate Pressure Overload–Induced Heart Failure, Chelsea L. Organ, Hiroyuki Otsuka, Shashi Bhushan, Zeneng Wang, Jessica Bradley, Rishi Trivedi, David J. Polhemus, W.H. Wilson Tang, Yuping Wu, Stanley L. Hazen, David J. Lefer

Mathematics and Statistics Faculty Publications

Background—Trimethylamine N-oxide (TMAO), a gut microbe–dependent metabolite of dietary choline and other trimethylamine-containing nutrients, is both elevated in the circulation of patients having heart failure and heralds worse overall prognosis. In animal studies, dietary choline or TMAO significantly accelerates atherosclerotic lesion development in ApoE-deficient mice, and reduction in TMAO levels inhibits atherosclerosis development in the low-density lipoprotein receptor knockout mouse. Methods and Results—C57BL6/J mice were fed either a control diet, a diet containing choline (1.2%) or a diet containing TMAO (0.12%) starting 3 weeks before surgical transverse aortic constriction. Mice were studied for 12 weeks after transverse aortic constriction. Cardiac …

Elevated Soluble Fms-Like Tyrosine Kinase-1 And Placental-Like Growth Factor Levels Are Associated With Development And Mortality Risk In Heart Failure, Muhammad Hammadah, Vasiliki V. Georgiopoulou, Andreas P. Kalogeropoulos, Malory Weber, Xi Wang, Michael A. Samara, Yuping Wu, Javed Butler, W.H. Wilson Tang

Mathematics and Statistics Faculty Publications

Background—Vascular endothelial dysfunction may play an important role in the progression of heart failure (HF). We hypothesize that elevated levels of vascular markers, placental-like growth factor, and soluble Fms-like tyrosine kinase-1 (sFlt-1) are associated with adverse outcomes in patients with HF. We also assessed possible triggers of sFlt-1 elevation in animal HF models. Methods and Results—We measured plasma placental-like growth factor and sFlt-1 in 791 HF patients undergoing elective coronary angiogram. Median (interquartile range) placental-like growth factor and sFlt-1 levels were 24 (20–29) and 382 (277–953) pg/mL, respectively. After 5 years of follow-up, and after using receiver operator characteristic curves …

Modeling Cross-Contamination During Poultry Processing: Dynamics In The Chiller Tank, Daniel Munther, Xiaodan Sun, Yanni Xiao, Sanyi Tang, Helio Shimozako, Jianhong Wu, Ben A. Smith, Aamir Fazil

Mathematics and Statistics Faculty Publications

Understanding mechanisms of cross-contamination during poultry processing is vital for effective pathogen control. As an initial step toward this goal, we develop a mathematical model of the chilling process in a typical high speed Canadian processing plant. An important attribute of our model is that it provides quantifiable links between processing control parameters and microbial levels, simplifying the complexity of these relationships for implementation into risk assessment models. We apply our model to generic, non-pathogenic Escherichia coli contamination on broiler carcasses, connecting microbial control with chlorine sanitization, organic load in the water, and pre-chiller E. coli levels on broiler carcasses. …

Prognostic Value Of Baseline And Changes In Circulating Soluble St2 Levels And The Effects Of Nesiritide In Acute Decompensated Heart Failure, W.H. Wilson Tang, Yuping Wu, Justin L. Grodin, Amy P. Hsu, Adrian F. Hernandez, Javed Butler, Marco Metra, Adriaan A. Voors, Michael G. Felker, Richard W. Troughton, Roger M. Mills, John J. Mcmurray, Paul W. Armstrong, Christopher M. O'Connor, Randall C. Starling

Mathematics and Statistics Faculty Publications

Objectives: The study sought to investigate the association between soluble growth stimulation expressed gene 2 (sST2) level and adverse outcomes in acute heart failure (HF). Background: Several studies have demonstrated the prognostic utility of sST2 levels in HF.Methods: sST2 levels were measured in sequential baseline and follow-up (48 to 72 h and 30 days) plasma samples from 858 acute HF subjects enrolled in the ASCEND-HF (Acute Study of Clinical Effectiveness of Nesiritide in Decompensated Heart Failure) trial biomarker substudy and were related to in-hospital and post-discharge clinical outcomes. Results: Higher sST2 levels were associated with increased death risk at 180 …

Curvature-Driven Foam Coarsening On A Sphere: A Computer Simulation, Shawn D. Ryan, Xiaoyu Zheng, Peter Palffy-Muhoray

Mathematics and Statistics Faculty Publications

The von Neumann-Mullins law for the area evolution of a cell in the plane describes how a dry foam coarsens in time. Recent theory and experiment suggest that the dynamics are different on the surface of a three-dimensional object such as a sphere. This work considers the dynamics of dry foams on the surface of a sphere. Starting from first principles, we use computer simulation to show that curvature-driven motion of the cell boundaries leads to exponential growth and decay of the areas of cells, in contrast to the planar case where the growth is linear. We describe the evolution …

Unraveling The Dose-Response Puzzle Of L. Monocytogenes: A Mechanistic Approach, S. M.Ashrafur Rahman, Daniel Munther, Aamir Fazil, Ben Smith, Jianhong Wu

Mathematics and Statistics Faculty Publications

Food-borne disease outbreaks caused by Listeria monocytogenes continue to impose heavy burdens on public health in North America and globally. To explore the threat L. monocytogenes presents to the elderly, pregnant woman and immuno-compromised individuals, many studies have focused on in-host infection mechanisms and risk evaluation in terms of dose-response outcomes. However, the connection of these two foci has received little attention, leaving risk prediction with an insufficient mechanistic basis. Consequently, there is a critical need to quantifiably link in-host infection pathways with the dose-response paradigm. To better understand these relationships, we propose a new mathematical model to describe the …

The Neural Dynamics Of Somatosensory Processing And Adaptation Across Childhood: A High-Density Electrical Mapping Study, Neha Uppal, John J. Foxe, John Butler, Frantzy Acluche, Sophie Molholm

Articles

Young children are often hyperreactive to somatosensory inputs hardly noticed by adults, as exemplified by irritation to seams or labels in clothing. The neurodevelopmental mechanisms underlying changes in sensory reactivity are not well understood. Based on the idea that neurodevelopmental changes in somatosensory processing and/or changes in sensory adaptation might underlie developmental differences in somatosensory reactivity, high-density electroencephalography was used to examine how the nervous system responds and adapts to repeated vibrotactile stimulation over childhood. Participants aged 6–18 yr old were presented with 50-ms vibrotactile stimuli to the right wrist over the median nerve at 5 blocked interstimulus intervals (ranging …

Mathematics Learning Support Across A Multi-Campus Institution: A Prototype Of Virtual Support, Cormac Breen, Ciaran O'Sullivan, Damian Cox

Articles

In this paper, a study on Mathematics Learning Support (MLS) that was undertaken across three institutes intending to form the Technological University for Dublin is outlined. This study consisted of a survey that was circulated to both staff and students in each of the three institutes. The survey had two objectives. Firstly it sought to identify the students’ needs for MLS in each of the three institutes. Secondly, it sought to ascertain the preferred method of provision of MLS, on a scale ranging from exclusively online, to exclusively in person. Following on the results of this survey it was decided …

On A Question About Almost Prime Ideals, Esmaeil Rostami, Reza Nekooei

Turkish Journal of Mathematics

In this paper, by giving an example we answer positively the question ``Does there exist a $P$-primary ideal $I$ in a Noetherian domain $R$ such that $PI = I^2$, but $I$ is not almost prime?", asked by S. M. Bhatwadekar and P. K. Sharma. We also investigated conditions under which the answer to the above mentioned question is negative.

The Wright Message, 2016-2017, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Alumni and Friends
-- A Tribute for Karen Sabey
-- The 2016 Hari Shankar Lecture
-- Faculty Spotlight
-- Around Wright Hall
-- Alumni Spotlight
-- CTLM News
-- Interview with Allysen Lovstuen
-- Students Spotlight
-- Donor Spotlight
-- Contributions to an Account - Recognition
-- Department Funds

1. Measuring Speed, Ruth Dover

More on Derivatives

Tables of values to measure rates.

Series 05, Ruth Dover

Series

Popular Maclaurin series and using substitution to create new series.

1. Coffee, Ruth Dover

Differential Equations

Newton’s Law of Cooling.