Mathematics Commons^™

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 …

Convergence Analysis And Error Estimates For A Second Order Accurate Finite Element Method For The Cahn–Hilliard–Navier–Stokes System, Amanda E. Diegel, Cheng Wang, Xiaoming Wang, Steven M. Wise

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we present a novel second order in time mixed finite element scheme for the Cahn–Hilliard–Navier–Stokes equations with matched densities. the scheme combines a standard second order Crank–Nicolson method for the Navier–Stokes equations and a modification to the Crank–Nicolson method for the Cahn–Hilliard equation. in particular, a second order Adams-Bashforth extrapolation and a trapezoidal rule are included to help preserve the energy stability natural to the Cahn–Hilliard equation. We show that our scheme is unconditionally energy stable with respect to a modification of the continuous free energy of the PDE system. Specifically, the discrete phase variable is shown …

Interproximal Distance Analysis Of Stereolithographic Casts Made By Cad-Cam Technology: An In Vitro Study, Melanie Hoffman, Seok-Hwan Cho, Naveen K. Bansal

Mathematics, Statistics and Computer Science Faculty Research and Publications

Statement of problem

The accuracy of interproximal distances of the definitive casts made by computer-aided design and computer-aided manufacturing (CAD-CAM) technology is not yet known.

Purpose

The purpose of this in vitro study was to compare the interproximal distances of stereolithographic casts made by CAD-CAM technology with those of stone casts made by the conventional method.

Material and methods

Dentoform teeth were prepared for a single ceramic crown on the maxillary left central incisor, a 3-unit fixed dental prosthesis (FDP) on the second premolar for a metal-ceramic crown, and a maxillary right first molar for a metal crown. Twenty digital …

Dodrant-Homomorphic Encryption For Cloud Databases Using Table Lookup, Thomas Schwarz

Mathematics, Statistics and Computer Science Faculty Research and Publications

Users of large commercial databases increasingly want to outsource their database operations to a cloud service providers, but guaranteeing the privacy of data in an outsourced database has become the major obstacle to this move. Encrypting all data solves the privacy issue, but makes many operations on the data impossible in the cloud, unless the service provider has the capacity to decrypt data temporarily. Homomorphic encryption would solve this issue, but despite great and on-going progress, it is still far from being operationally feasible. In 2015, we presented what we now call dodrant-homomorphic encryption, a method that encrypts numeric values …

A Bivariate Hypothesis Testing Approach For Mapping The Trait-Influential Gene, Garrett Saunders, Matthew D. Meng, John R. Stevens

Mathematics and Statistics Faculty Publications

The linkage disequilibrium (LD) based quantitative trait loci (QTL) model involves two indispensable hypothesis tests: the test of whether or not a QTL exists, and the test of the LD strength between the QTaL and the observed marker. The advantage of this two-test framework is to test whether there is an influential QTL around the observed marker instead of just having a QTL by random chance. There exist unsolved, open statistical questions about the inaccurate asymptotic distributions of the test statistics. We propose a bivariate null kernel (BNK) hypothesis testing method, which characterizes the joint distribution of the two test …

On Congruence Lattices Of Nilsemigroups, Alexander L. Popovich, Peter Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

We prove that the congruence lattice of a nilsemigroup is modular if and only if the width of the semigroup, as a poset, is at most two, and distributive if and only if its width is one. In the latter case, such semigroups therefore coincide with the nil Δ">Δ Δ -semigroups. It is further shown that if a finitely generated nilsemigroup has modular congruence lattice, then the semigroup is finite.

The Double-Edged Sword: A Mixed Methods Study Of The Interplay Between Bipolar Disorder And Technology Use, Mark Matthews, Elizabeth Murnane, Jaime Snyder, Shion Guha, Pamara Chang, Gavin Doherty, Geri K. Gay

Mathematics, Statistics and Computer Science Faculty Research and Publications

Human behavior is increasingly reflected or acted out through technology. This is of particular salience when it comes to changes in behavior associated with serious mental illnesses including schizophrenia and bipolar disorder. Early detection is crucial for these conditions but presently very challenging to achieve. Potentially, characteristics of these conditions' traits and symptoms, at both idiosyncratic and collective levels, may be detectable through technology use patterns. In bipolar disorder specifically, initial evidence associates changes in mood with changes in technology-mediated communication patterns. However much less is known about how people with bipolar disorder use technology more generally in their lives, …

Implant Treatment In The Predoctoral Clinic: A Retrospective Database Study Of 1091 Patients, Soni Prasad, Christopher Hambrook, Eric Reigle, Katherine Sherman, Naveen K. Bansal, Arthur F. Hefti

Mathematics, Statistics and Computer Science Faculty Research and Publications

Purpose: This retrospective study was conducted at the Marquette University School of Dentistry to (1) characterize the implant patient population in a predoctoral clinic, (2) describe the implants inserted, and (3) provide information on implant failures.

Materials and Methods: The study cohort included 1091 patients who received 1918 dental implants between 2004 and 2012, and had their implants restored by a crown or a fixed dental prosthesis. Data were collected from patient records, entered in a database, and summarized in tables and figures. Contingency tables were prepared and analyzed by a chi-squared test. The cumulative survival probability of implants was …

Magnetic Control Of Lateral Migration Of Ellipsoidal Microparticles In Microscale Flows, R. Zhou, C. A. Sobecki, J. Zhang, Yanzhi Zhang, Cheng Wang

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Merging Peg Solitaire In Graphs, John Engbers, Ryan Weber

Mathematics, Statistics and Computer Science Faculty Research and Publications

Peg solitaire has recently been generalized to graphs. Here, pegs start on all but one of the vertices in a graph. A move takes pegs on adjacent vertices x and y, with y also adjacent to a hole on vertex z, and jumps the peg on x over the peg ony to z, removing the peg on y. The goal of the game is to reduce the number of pegs to one.

We introduce the game merging peg solitaire on graphs, where a move takes pegs on vertices x and z (with a hole on y) and merges them to …

A Perspective On The Challenges And Issues In Developing Biomarkers For Human Allergic Risk Assessments, Ying Mu, Dianne E. Godar, Stephen Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Failure Of Care Acquisition: Identifying Risk Factors In American Health Disparities, Nicholas Downing, Mamunur Rashid

Student Research

We examined the effects of various demographic and socioeconomic risk factors that influence an adult's decision not to obtain medical care in the United States utilizing data from the 2015 National Health Interview Survey (NHIS). Bivariate analysis and multivariate logistic regression revealed that family income, insurance status and whether one worries about paying medical bills make individuals nearly 80% less likely to obtain care than their counterparts. This study provides evidence that certain risk factors, especially those directly related to one's socioeconomic status, may put individuals at greater risk for failure to obtain care. Interventions in policy may be needed …

A Privacy Preserving Framework For Rfid Based Healthcare Systems, Farzana Rahman, Anwarul A. Bhuiyan, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

RFID (Radio Frequency IDentification) is anticipated to be a core technology that will be used in many practical applications of our life in near future. It has received considerable attention within the healthcare for almost a decade now. The technology’s promise to efficiently track hospital supplies, medical equipment, medications and patients is an attractive proposition to the healthcare industry. However, the prospect of wide spread use of RFID tags in the healthcare area has also triggered discussions regarding privacy, particularly because RFID data in transit may easily be intercepted and can be send to track its user (owner). In a …

Educational Magic Tricks Based On Error-Detection Schemes, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

Magic tricks based on computer science concepts help grab student attention and can motivate them to delve more deeply. Error detection ideas long used by computer scientists provide a rich basis for working magic; probably the most well known trick of this type is one included in the CS Unplugged activities. This paper shows that much more powerful variations of the trick can be performed, some in an unplugged environment and some with computer assistance. Some of the tricks also show off additional concepts in computer science and discrete mathematics.

A Direct D-Bar Method For Partial Boundary Data Electrical Impedance Tomography With A Priori Information, Melody Alsaker, Sarah J. Hamilton, Andreas Hauptmann

Mathematics, Statistics and Computer Science Faculty Research and Publications

Electrical Impedance Tomography (EIT) is a non-invasive imaging modality that uses surface electrical measurements to determine the internal conductivity of a body. The mathematical formulation of the EIT problem is a nonlinear and severely ill-posed inverse problem for which direct D-bar methods have proved useful in providing noise-robust conductivity reconstructions. Recent advances in D-bar methods allow for conductivity reconstructions using EIT measurement data from only part of the domain (e.g., a patient lying on their back could be imaged using only data gathered on the accessible part of the body). However, D-bar reconstructions suffer from a loss of sharp edges …

Comparing Grounded Theory And Topic Modeling: Extreme Divergence Or Unlikely Convergence?, Eric P.S. Baumer, David Mimno, Shion Guha, Emily Quan, Geri K. Gay

Mathematics, Statistics and Computer Science Faculty Research and Publications

Researchers in information science and related areas have developed various methods for analyzing textual data, such as survey responses. This article describes the application of analysis methods from two distinct fields, one method from interpretive social science and one method from statistical machine learning, to the same survey data. The results show that the two analyses produce some similar and some complementary insights about the phenomenon of interest, in this case, nonuse of social media. We compare both the processes of conducting these analyses and the results they produce to derive insights about each method's unique advantages and drawbacks, as …

Symptom Levels In Care-Seeking Bangladeshi And Nepalese Adults With Advanced Cancer, Richard Love, Tahmina Ferdousy, Bishnu D. Paudel, Shamsun Nahar, Rumana Dowla, Mohammad Adibuzzaman, Golam Mushih Tanimul Ahsan, Miftah Uddin, Reza Selim, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

Purpose

Three-fourths of patients with advanced cancer are reported to suffer from pain. A primary barrier to provision of adequate symptom treatment is failure to appreciate the intensity of the symptoms patients are experiencing. Because data on Bangladeshi and Nepalese patients’ perceptions of their symptomatic status are limited, we sought such information using a cell phone questionnaire.

Methods

At tertiary care centers in Dhaka and Kathmandu, we recruited 640 and 383 adult patients, respectively, with incurable malignancy presenting for outpatient visits and instructed them for that single visit on one-time completion of a cell phone platform 15-item survey of questions …

Physiological Health Parameters Among College Students To Promote Chronic Disease Prevention And Health Promotion, David R. Black, Daniel C. Coster, Samantha R. Paige

Mathematics and Statistics Faculty Publications

This study aimed to provide physiologic health risk parameters by gender and age among college students enrolled in a U.S. Midwestern University to promote chronic disease prevention and ameliorate health. A total of 2615 college students between 18 and 25 years old were recruited annually using a series of cross-sectional designs during the spring semester over an 8-year period. Physiologic parameters measured included body mass index (BMI), percentage body fat (%BF), blood serum cholesterol (BSC), and systolic (SBP) and diastolic (DBP) blood pressure. These measures were compared to data from NHANES to identify differences in physiologic parameters among 18-25 year …

Eit Imaging Of Admittivities With A D-Bar Method And Spatial Prior: Experimental Results For Absolute And Difference Imaging, Sarah J. Hamilton

Mathematics, Statistics and Computer Science Faculty Research and Publications

Electrical impedance tomography (EIT) is an emerging imaging modality that uses harmless electrical measurements taken on electrodes at a body's surface to recover information about the internal electrical conductivity and or permittivity. The image reconstruction task of EIT is a highly nonlinear inverse problem that is sensitive to noise and modeling errors making the image reconstruction task challenging. D-bar methods solve the nonlinear problem directly, bypassing the need for detailed and time-intensive forward models, to provide absolute (static) as well as time-difference EIT images. Coupling the D-bar methodology with the inclusion of high confidence a priori data results in a …

Weighted Distributions: A Brief Review, Perspective And Characterizations, Aamir Saghir, Gholamhossein G. Hamedani, Sadaf Tazeem, Aneeqa Khadim

Mathematics, Statistics and Computer Science Faculty Research and Publications

The weighted distributions are widely used in many fields such as medicine, ecology and reliability, to name a few, for the development of proper statistical models. Weighted distributions are milestone for efficient modeling of statistical data and prediction when the standard distributions are not appropriate. A good deal of studies related to the weight distributions have been published in the literature. In this article, a brief review of these distributions is carried out. Implications of the differing weight models for future research as well as some possible strategies are discussed. Finally, characterizations of these distributions based on a simple relationship …

Oscillation Criteria For Third-Order Nonlinear Functional Difference Equations With Damping, Martin Bohner, C. Dharuman, R. Srinivasan, Ethiraju Thandapani

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we obtain some new criteria for the oscillation of certain third-order difference equations using comparison principles with a suitable couple of first-order difference equations. The presented results improve and extend the earlier ones. Examples are provided to illustrate the main results.

The Value Of A Win: Analysis Of Playoff Structures, Matthew Orsi

Honors Projects in Mathematics

The purpose of this Senior Capstone project is to analyze the distinctions between existing playoff systems. In particular, we are looking to analyze the differences between the standard single-elimination tournament (which the NCAA has used since the inception of the tournament) and other potential options: double-elimination and multiple game series. Popular sports such as Major League Baseball and the National Basketball Association all use multiple game series for their playoffs. This project will use probability theory and simulation to determine the likelihood of different seeds winning a championship as well as the expected number of victories by seed in each …

Stationary Acceleration Of Frenet Curves, Nemat Abazari, Martin Bohner, Ilgin Sager, Yusuf Yayli

Mathematics and Statistics Faculty Research & Creative Works

In this paper, the stationary acceleration of the spherical general helix in a 3-dimensional Lie group is studied by using a bi-invariant metric. The relationship between the Frenet elements of the stationary acceleration curve in 4-dimensional Euclidean space and the intrinsic Frenet elements of the Lie group is outlined. As a consequence, the corresponding curvature and torsion of these curves are computed. In Minkowski space, for the curves on a timelike surface to have a stationary acceleration, a necessary and sufficient condition is refined.

Deriving A Provisional Tolerable Intake For Intravenous Exposure To Silver Nanoparticles Released From Medical Devices, Laura C. Savery, Rene Vinas, Amber M. Nagy, Prachi Pradeep, Stephen Merrill, Subhas G. Malghan, Peter L. Goering, Ronald P. Brown

Mathematics, Statistics and Computer Science Faculty Research and Publications

Silver nanoparticles (AgNP) are incorporated into medical devices for their anti-microbial characteristics. The potential exposure and toxicity of AgNPs is unknown due to varying physicochemical particle properties and lack of toxicological data. The aim of this safety assessment is to derive a provisional tolerable intake (pTI) value for AgNPs released from blood-contacting medical devices. A literature review of in vivo studies investigating critical health effects induced from intravenous (i. v.) exposure to AgNPs was evaluated by the Annapolis Accords principles and Toxicological Data Reliability Assessment Tool (ToxRTool). The point of departure (POD) was based on an i. v. 28-day …

Predoctoral Dental Students’ Perceptions Of Dental Implant Training: Effect Of Preclinical Simulation And Clinical Experience, Soni Prasad, Naveen K. Bansal

School of Dentistry Faculty Research and Publications

The aims of this study were to assess 1) differences in perceptions of dental implant training between dental students who received didactic training alone (control group) and those who received didactic plus simulation training (test group); 2) differences in response between students with and without clinical experience in implant dentistry; and 3) the interaction effect of simulation training and clinical experience on students’ satisfaction. A survey was distributed to the control group in 2014 and to the test group in 2015; both groups were at the same U.S. dental school. Data were collected on confidence levels with various implant restorative …

Lies, Statistics, Mathematics And The Truth, Nathan L. Tintle

Faculty Work Comprehensive List

"Recognizing a key distinction between mathematics and statistics is helpful in understanding how we know if a statement is true."

Posting about deductive and inductive reasoning­­­­­­­­ from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world.

http://inallthings.org/lies-statistics-mathematics-and-the-truth/

Mass Action In Two-Sex Population Models: Encounters, Mating Encounters And The Associated Numerical Correction, Katherine Snyder, Brynja R. Kohler, Luis F. Gordillo

Mathematics and Statistics Faculty Publications

Ideal gas models are a paradigm used in Biology for the phenomenological modelling of encounters between individuals of different types. These models have been used to approximate encounter rates given densities, velocities and distance within which an encounter certainly occurs. When using mass action in two-sex populations, however, it is necessary to recognize the difference between encounters and mating encounters. While the former refers in general to the (possibly simultaneous) collisions between particles, the latter represents pair formation that will produce offspring. The classical formulation of the law of mass action does not account this difference. In this short paper, …

Application Of Inverse Problems In Imaging, Xiaoyue Luo

Post-Grant Reports

In this project, we studied how to enhance image quality by denoising and deblurring a given image mathematically. We compared some existing state-of-the-art methods for image denoising and deblurring. We implemented the algorithms numerically using Matlab.

We studied the possibility of combining statistical analysis with the traditional image restoration methods including using wavelets and framelets and we derived some encouraging preliminary results.

My research student Alleta Maier gave a sequence of talks on the project including the Pacific Northwest Mathematical Association of America conference at Oregon State University in April, 2016; Linfield College Taylor Series in March, 2016, and Linfield …

Sexual Dimorphism In Digit Ratios Derived From Dorsal Digit Length Among Adults And Children, Sanjay Kumar, Martin Voracek, Maharaj Singh

Mathematics, Statistics and Computer Science Faculty Research and Publications

Sexual dimorphism in ventrally measured digit ratios (2D:4D and other) has been related to prenatal sex-hormone levels. In the present series of three studies, we measured all digit lengths (excluding the thumb) on the dorsal, rather than the ventral, side of left and right hands and investigated the sexual dimorphism in digit ratios in three independent samples, two of them comprising adults (Study I, N = 104; Study II, N = 154), and one further, comprising kindergarten children (Study III, N = 64). Results show that men have lower digit-ratio values compared to women in digit ratios that include digit …

An Online Educational Program Improves Pediatric Oncology Nurses’ Knowledge, Attitudes, And Spiritual Care Competence, Cheryl L. Petersen, Margaret Callahan, Donna O. Mccarthy, Ronda G. Hughes, Rosemary White-Traut, Naveen K. Bansal

Mathematics, Statistics and Computer Science Faculty Research and Publications

This study evaluated the potential impact of an online spiritual care educational program on pediatric nurses’ attitudes toward and knowledge of spiritual care and their competence to provide spiritual care to children with cancer at the end of life. It was hypothesized that the intervention would increase nurses’ positive attitudes toward and knowledge of spiritual care and increase nurses’ level of perceived spiritual care competence. A positive correlation was expected between change in nurses’ perceived attitudes toward and knowledge of spiritual care and change in nurses’ perceived spiritual care competence. A prospective, longitudinal design was employed, and analyses included one-way …