Mathematics ThesesCopyright (c) 2017 Georgia State University All rights reserved.
https://scholarworks.gsu.edu/math_theses
Recent documents in Mathematics Thesesen-usFri, 08 Dec 2017 02:02:17 PST3600Sign Patterns of J-orthogonal Matrices
https://scholarworks.gsu.edu/math_theses/159
https://scholarworks.gsu.edu/math_theses/159Wed, 06 Dec 2017 06:17:08 PST
This thesis builds upon the results in “G-matrices, J-orthogonal matrices, and their sign patterns”, Czechoslovak Math. J. 66 (2016), 653-670, by Hall and Rozloˇzn ́ık. Some general results about the sign patterns of J-orthogonal matrices are proved, including about block diagonal matrices. It is shown that every full 4 × 4 sign pattern allows J -orthogonality and as a result that, for n ≤ 4, all n × n full sign patterns allow a J-orthogonal matrix as well as a G-matrix. The 3 × 3 sign patterns of the J -orthogonal matrices which have zero entires are also characterized.
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Caroline ParnassA MATHEMATICAL MODEL OF THE HUMAN CARDIAC SODIUM CHANNEL
https://scholarworks.gsu.edu/math_theses/158
https://scholarworks.gsu.edu/math_theses/158Fri, 21 Jul 2017 05:52:13 PDT
Sodium ion (Na+) channels play an important role in excitable cells, as they are responsible for the initiation of action potentials. Understanding the electrical characteristics of sodium channels is essential in predicting their behavior under different physiological conditions. We investigated several Markov models for the human cardiac sodium channel (NaV1.5) to derive a minimal mathematical model that can describe the reported experimental data obtained using major voltage-clamp protocols. We obtained simulation results for current-voltage relationships, steady-state inactivation, the voltage dependence of normalized ion channel conductance; activation and deactivation, fast and slow inactivation and recovery from inactivation kinetics. Good agreement with the experimental data provides us with the mechanisms of the fast and slow inactivation of the human sodium channel and the coupling of its inactivation states to the closed and open states in the activation pathway.
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Tesfaye AsfawDifferences Of Diabetes-Related Complications And Diabetes Preventive Health Care Utilization In Asian And White Using Multiple Years National Health Survey Data
https://scholarworks.gsu.edu/math_theses/157
https://scholarworks.gsu.edu/math_theses/157Mon, 10 Apr 2017 09:27:22 PDT
The main purpose of this study is to examine the differences of preventive management utilizations and diabetes complications in Asian Americans and Non-Hispanic whites using multiple years (2002-2013) Behavioral Risk Factor Surveillance System (BRFSS). SAS for complex survey procedures were used to perform the data analysis. Odds ratios (OR) were calculated to compare the prevalence of diabetes complications and preventive management rate in Asian with white. Compared to white, the prevalence of diabetes retinopathy in Asians were higher, while the rates of neuropathy and cardiovascular complications, pneumonia shot, personally management as well as management diabetes with doctors were lower. The prevalence of routine checkup in Asian was not significantly different from the prevalence in white. More attentions should be paid on Asians for diabetes related retinopathy.
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Yonggang LiDefining the Inflammation Biomarkers of Inflammatory Bowel Diseases and Colorectal Carcinomas
https://scholarworks.gsu.edu/math_theses/156
https://scholarworks.gsu.edu/math_theses/156Mon, 05 Dec 2016 18:46:42 PST
Ulcerative colitis (UC) and Crohn’s disease (CD) are the two common forms of inflammatory bowel disease (IBD). They share similar clinical and demographic features as well as harbor key differences in tissue damage and prognosis. Previous studies indicated that they contributed to the increased rick to Colorectal cancer (CRC). However, whether UC and CD share inflammatory signatures still remains controversial. In addition, no inflammatory signatures have been reported on CRC. To answer these questions, a comprehensive study has been conducted on collected microarray datasets. Our analysis suggests that although CD and UC share common inflammatory pathways, they also present difference. Especially, CD patients are likely to have type I response, while UC patients are inclined to undergo type II response. Pathway enrichment analysis on CRC uncovered two potential CRC-specific inflammatory pathways.
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Jianxu LiSeeking Direct Coastal Erosion Associated Factors in the United States Shorelines
https://scholarworks.gsu.edu/math_theses/155
https://scholarworks.gsu.edu/math_theses/155Tue, 29 Nov 2016 10:08:38 PST
Sea-level rise is projected to have a wide range of effects on coastal environments, developments, and infrastructure. Based on the U.S. Geological Survey (USGS) Coastal Vulnerability Index (CVI) system data, we developed a two-stage model; firstly, the Bayesian Network (BN) is used to define relationship among driving forces; secondly, the logistic regression is used to evaluate direct association for direct factors related to Shoreline Erosion. Using this two-stage approach, increased sea-level (OR: 4.03[3.72,4.38]), higher Wave Height (OR: 0.56[0.54,0.61]), smaller Tidal Range (OR: 1.68[1.52,1.87]) and smaller Coastal Slope (OR: 0.45[0.44,0.49]) are directly associated with Shoreline Erosion in Atlantic Ocean; Geomorphology setting (OR: 9.35[6.33,14.18]) in high risk regions, such as beaches, is identified as direct association with Shoreline Erosion in Gulf of Mexico; Smaller tidal range (OR: 0.10[0.04,0.27] directly associated with Shoreline Erosion in Pacific Ocean. These direct factors were evaluated predictive ability with accuracy rates 0.59 and AUC 0.63.
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Le Chen et al.Identifying Inflammatory Bowel Disease Patients in TCGA Database
https://scholarworks.gsu.edu/math_theses/154
https://scholarworks.gsu.edu/math_theses/154Mon, 25 Jul 2016 09:47:09 PDT
Chronic inflammation increases the risk of developing cancer. We aim to investigate the molecular pathway of inflammation induced cancer by comparing gene expression in colorectal (CRC) tumors of patients with inflammatory bowel disease (IBD) to sporatic colorectal tumors. Since mRNA microarray data of IBD induced CRC is not readily available, we attempt to isolate IBD patients in a public database based on their gene expression signatures.
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Regina ChangSpatial Analysis of Retinal Pigment Epithelium Morphology
https://scholarworks.gsu.edu/math_theses/153
https://scholarworks.gsu.edu/math_theses/153Mon, 06 Jun 2016 08:42:10 PDT
In patients with age-related macular degeneration, a monolayer of cells in the eyes called retinal pigment epithelium differ from healthy ones in morphology. It is therefore important to quantify the morphological changes, which will help us better understand the physiology, disease progression and classification. Classification of the RPE morphometry has been accomplished with whole tissue data. In this work, we focused on the spatial aspect of RPE morphometric analysis. We used the second-order spatial analysis to reveal the distinct patterns of cell clustering between normal and diseased eyes for both simulated and experimental human RPE data. We classified the mouse genotype and age by the k-Nearest Neighbors algorithm. Radially aligned regions showed different classification power for several cell shape variables. Our proposed methods provide a useful addition to classification and prognosis of eye disease noninvasively.
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Haitao HuangJackknife Empirical Likelihood for the Concordance Correlation Coefficient
https://scholarworks.gsu.edu/math_theses/152
https://scholarworks.gsu.edu/math_theses/152Wed, 27 Apr 2016 12:27:20 PDT
The concordance correlation coefficient (CCC) is a common measure of reproducibility or agreement between data values in paired samples. Confidence intervals and hypothesis tests of the CCC using normal approximations (NA) have been shown to have poor coverage for highly skewed distributions. This study applies the jackknife empirical likelihood (JEL) to confidence intervals for the CCC and compares coverage probability and interval length for JEL and NA methods. Data are simulated for CCC values between 0.25 - 0.95 from normal and non-normal distributions of varying skewness. Simulation results showed that JEL methods perform better than the NA methods particularly with data from skewed distributions.The JEL methods have the widest confidence intervals in most cases. Application of JEL methods are illustrated by evaluating concordance between self-reported and clinically measured body weight and height from the National Health and Nutrition Examination Survey (NHANES).
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Anna MossNumerical Solutions to Two-Dimensional Integration Problems
https://scholarworks.gsu.edu/math_theses/151
https://scholarworks.gsu.edu/math_theses/151Tue, 08 Dec 2015 08:37:13 PST
This paper presents numerical solutions to integration problems with bivariate integrands. Using equally spaced nodes in Adaptive Simpson's Rule as a base case, two ways of sampling the domain over which the integration will take place are examined. Drawing from Ouellette and Fiume, Voronoi sampling is used along both axes of integration and the corresponding points are used as nodes in an unequally spaced degree two Newton-Cotes method. Then the domain of integration is triangulated and used in the Triangular Prism Rules discussed by Limaye. Finally, both of these techniques are tested by running simulations over heavily oscillatory and monomial (up to degree five) functions over polygonal regions.
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Alexander CarstairsAccurate Approximation Series for Optimal Targeting Regions in a Neural Growth Model with a Low –branching Probability
https://scholarworks.gsu.edu/math_theses/150
https://scholarworks.gsu.edu/math_theses/150Thu, 03 Dec 2015 08:22:14 PST
Understanding the complex growth process of dendritic arbors is essential for the medical field and disciplines like Biology and Neurosciences. The establishment of the dendritic patterns has received increasing attention from experimental researchers that seek to determine the cellular mechanisms that play a role in the growth of neural trees. Our goal in this thesis was to prove the recurrence formula for the probability distribution of all possible neural trees, as well as the formulas of the expected number of active branches and their variances. We also derived formulas for the spatial locations of the optimal targeting region for a tree with branching probability. These formulas were necessary for the simplified stochastic computational model that Osan et al have developed in order to examine how changes in branching probability influence the success of targeting neurons located at different distances away from a starting point.
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Bernardo NietoTrends in Herpes Zoster Incidence from 1940 to 2008 Using a Cross-sectional Survey
https://scholarworks.gsu.edu/math_theses/149
https://scholarworks.gsu.edu/math_theses/149Mon, 30 Nov 2015 08:32:07 PST
Previous healthcare-based studies have reported increasing herpes zoster (HZ) incidence over time; however, this could be an artifact of increased healthcare utilization. This study is a cross-sectional analysis of 15,103 respondents in the 2008 wave of the Health and Retirement Study (HRS) to evaluate changes in HZ incidence from 1940 to 2008. Negative binomial regression is used to model the effect of calendar year, age of onset of HZ, gender and race/ethnicity on HZ incidence. A nonparametric method based on B-spline basis expansion is used to model the effect of calendar year to avoid imposing a predetermined functional form and produce flexible and accurate estimates. This study demonstrates increasing HZ incidence from 1940 to 2008 using self-reported HZ. Although the reason for this increase remains unknown, this study supports the assertion that this trend is real and not an artifact of increasing healthcare utilization for HZ over time.
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Craig HalesDietary Sodium Intake and Mortality among US Older Adults: The Third National Health and Nutrition Examination Survey
https://scholarworks.gsu.edu/math_theses/148
https://scholarworks.gsu.edu/math_theses/148Tue, 25 Aug 2015 09:16:54 PDT
Strong evidence has linked dietary sodium intake to blood pressure, but the effects of sodium intake on cardiovascular diseases (CVD) outcomes remain elusive, especially for older population. We examined the association between estimated usual sodium intake and CVD and all-cause mortality in a nationally representative sample of 4068 US adults aged 51 and older surveyed in 1988-1994. After a mean follow-up of 12.9 years from 1988 to 2006, 1680 participants died: 734 from CVD; 392 from ischemic heart disease (IHD); and 144 from stroke. In the Cox proportional models adjusted for sociodemographic variables and CVD risk factors, sodium intake was not significantly associated with all-cause, CVD, IHD and stroke mortality. No significant interactions were observed between sodium intake and sex, race/ethnicity, hypertension status, body mass index or physical activity for any of the outcomes studied. However, among Mexican-Americans sodium intake was significantly and linearly associated with CVD mortality.
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Lixia ZhaoMultinomial Logistic Regression Analysis Of Varicella Vaccination - 2011 National Immunization Survey (NIS) – Teen Survey Data
https://scholarworks.gsu.edu/math_theses/147
https://scholarworks.gsu.edu/math_theses/147Tue, 28 Apr 2015 09:37:13 PDT
The varicella-zoster virus (VZV) causes chickenpox or varicella, a disease primarily in children, and Herpes Zoster (HZ) or zoster or shingles, a disease that affects adults. A 2-dose Varicella vaccination is recommended in the United States, the first dose at age 15-18 months and the second dose at 4 to 6 years.In this study, we used multinomial logistic regression to analysis data from the 2011 National Immunization Survey-Teen (NIS-Teen) to identify factors that have a significant impact on the number of doses (0-dose, 1-dose, or 2-dose) a teen will have. We evaluate Varicella vaccination coverage stratified by Census region and assessed factors independently associated with varicella vaccination.
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Benjamin FreduaFrobenius-Like Permutations and Their Cycle Structure
https://scholarworks.gsu.edu/math_theses/146
https://scholarworks.gsu.edu/math_theses/146Fri, 24 Apr 2015 11:57:04 PDT
Polynomial functions over finite fields are a major tool in computer science and electrical engineering and have a long history. Some of its aspects, like interpolation and permutation polynomials are described in this thesis. A complete characterization of subfield compatible polynomials (f in E[x] such that f(K) is a subset of L, where K,L are subfields of E) was recently given by J. Hull. In his work, he introduced the Frobenius permutation which played an important role. In this thesis, we fully describe the cycle structure of the Frobenius permutation. We generalize it to a permutation called a monomial permutation and describe its cycle factorization. We also derive some important congruences from number theory as corollaries to our work.
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Adil B. ViraniEmpirical Likelihood Confidence Intervals for the Population Mean Based on Incomplete Data
https://scholarworks.gsu.edu/math_theses/145
https://scholarworks.gsu.edu/math_theses/145Fri, 24 Apr 2015 07:17:18 PDT
The use of doubly robust estimators is a key for estimating the population mean response in the presence of incomplete data. Cao et al. (2009) proposed an alternative doubly robust estimator which exhibits strong performance compared to existing estimation methods. In this thesis, we apply the jackknife empirical likelihood, the jackknife empirical likelihood with nuisance parameters, the profile empirical likelihood, and an empirical likelihood method based on the influence function to make an inference for the population mean. We use these methods to construct confidence intervals for the population mean, and compare the coverage probabilities and interval lengths using both the ``usual'' doubly robust estimator and the alternative estimator proposed by Cao et al. (2009). An extensive simulation study is carried out to compare the different methods. Finally, the proposed methods are applied to two real data sets.
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Jose Manuel Valdovinos AlvarezDiscrepancy Principle and Stable Parameter Estimation in Avian Influenza
https://scholarworks.gsu.edu/math_theses/144
https://scholarworks.gsu.edu/math_theses/144Fri, 05 Dec 2014 10:36:50 PST
In the case of a linear ill-posed problem with noisy data, a version of an a posteriori parameter selection discrepancy principle (DP) is justified for an arbitrary regularization strategy under very general assumptions on the operator and the stabilizer. Its efficiency is demonstrated for a practically important inverse problem in avian influenza. We refer to our result as an abstract discrepancy principle (ADP), which shows that applicability of the DP largely depends on the level of noise in the data rather than the method used for the construction of a specific regularization procedure.
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Linda DeCampData Mining Analysis of the Parkinson's Disease
https://scholarworks.gsu.edu/math_theses/143
https://scholarworks.gsu.edu/math_theses/143Fri, 05 Dec 2014 07:56:46 PST
Biological research is becoming increasingly database driven and statistical learning can be used to discover patterns in the biological data. In the thesis, the supervised learning approaches are utilized to analyze the Oxford Parkinson’s disease detection data and build models for prediction or classification. We construct predictive models based on training set, evaluate their performance by applying these models to an independent test set, and find the best methods for predicting whether people have Parkinson’s disease. The proposed artificial neural network procedure outperforms with the best and highest prediction accuracy, while the logistic and probit regressions are preferred statistical models which can offer better interpretation with the higher prediction accuracy compared to other proposed data mining approaches.
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Xiaoyuan WangA Mathematical Model For Population Dynamics of Antibiotic Treatment
https://scholarworks.gsu.edu/math_theses/142
https://scholarworks.gsu.edu/math_theses/142Thu, 04 Dec 2014 12:17:56 PST
The objective of the thesis is to model the behavior of the reaction between two species of bacteria and antibiotics by building an ordinary differential equation (ODE) system under a list of assumptions. With the ODE, we analyze equilibrium points and the stability of these equilibrium points to forecast the trend of each species of bacteria and antibiotics. We test the validity of the model assumptions. Based on these outcomes, we show that: 1. Both equilibrium points and eigenvalues differ in orders of magnitude. 2. Some figures which were generated using different initial values do not make any sense. 3. There were abnormal values of the variables sensitivity.
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siyu tianJackknife Empirical Likelihood Inference For The Pietra Ratio
https://scholarworks.gsu.edu/math_theses/140
https://scholarworks.gsu.edu/math_theses/140Wed, 03 Dec 2014 08:22:00 PST
Pietra ratio (Pietra index), also known as Robin Hood index, Schutz coefficient (Ricci-Schutz index) or half the relative mean deviation, is a good measure of statistical heterogeneity in the context of positive-valued data sets. In this thesis, two novel methods namely "adjusted jackknife empirical likelihood" and "extended jackknife empirical likelihood" are developed from the jackknife empirical likelihood method to obtain interval estimation of the Pietra ratio of a population. The performance of the two novel methods are compared with the jackknife empirical likelihood method, the normal approximation method and two bootstrap methods (the percentile bootstrap method and the bias corrected and accelerated bootstrap method). Simulation results indicate that under both symmetric and skewed distributions, especially when the sample is small, the extended jackknife empirical likelihood method gives the best performance among the six methods in terms of the coverage probabilities and interval lengths of the confidence interval of Pietra ratio; when the sample size is over 20, the adjusted jackknife empirical likelihood method performs better than the other methods, except the extended jackknife empirical likelihood method. Furthermore, several real data sets are used to illustrate the proposed methods.
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Yueju SuA Comparison of Two Modeling Techniques in Customer Targeting For Bank Telemarketing
https://scholarworks.gsu.edu/math_theses/139
https://scholarworks.gsu.edu/math_theses/139Tue, 02 Dec 2014 13:37:18 PST
Customer targeting is the key to the success of bank telemarketing. To compare the flexible discriminant analysis and the logistic regression in customer targeting, a survey dataset from a Portuguese bank was used. For the flexible discriminant analysis model, the backward elimination of explanatory variables was used with several rounds of manual re-defining of dummy variables. For the logistic regression model, the automatic stepwise selection was performed to decide which explanatory variables should be left in the final model. Ten-fold stratified cross validation was performed to estimate the model parameters and accuracies. Although employing different sets of explanatory variables, the flexible discriminant analysis model and the logistic regression model show equally satisfactory performances in customer classification based on the areas under the receiver operating characteristic curves. Focusing on the predicted “right” customers, the logistic regression model shows slightly better classification and higher overall correct prediction rate.
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Hong Tang