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Articles 1 - 22 of 22
Full-Text Articles in Mathematics
Transformation Groups And Duality In The Analysis Of Musical Structure, Janine Du Plessis
Transformation Groups And Duality In The Analysis Of Musical Structure, Janine Du Plessis
Mathematics Theses
One goal of music theory is to describe the resources of a pitch system. Traditionally, the study of pitch intervals was done using frequency ratios of the powers of small integers. Modern mathematical music theory offers an independent way of understanding the pitch system by considering intervals as transformations. This thesis takes advantage of the historical emergence of algebraic structures in musicology and, in the spirit of transformational theory, treats operations that form mathematical groups. Aspects of Neo-Riemannian theory are explored and developed, in particular the T/I and PLR groups as dual. Pitch class spaces, such as 12, can also …
Examination Of Initialization Techniques For Nonnegative Matrix Factorization, John Frederic
Examination Of Initialization Techniques For Nonnegative Matrix Factorization, John Frederic
Mathematics Theses
While much research has been done regarding different Nonnegative Matrix Factorization (NMF) algorithms, less time has been spent looking at initialization techniques. In this thesis, four different initializations are considered. After a brief discussion of NMF, the four initializations are described and each one is independently examined, followed by a comparison of the techniques. Next, each initialization's performance is investigated with respect to the changes in the size of the data set. Finally, a method by which smaller data sets may be used to determine how to treat larger data sets is examined.
Factorization Of Quasiseparable Matrices, Paul D. Johnson
Factorization Of Quasiseparable Matrices, Paul D. Johnson
Mathematics Theses
This paper investigates some of the ideas and algorithms developed for exploiting the structure of quasiseparable matrices. The case of purely scalar generators is considered initially. The process by which a quasiseparable matrix is represented as the product of matrices comprised of its generators is explained. This is done clearly in the scalar case, but may be extended to block generators. The complete factoring approach is then considered. This consists of two stages: inner-outer factorization followed by inner-coprime factorization. Finally, the stability of the algorithm is investigated. The algorithm is used to factor various quasiseparable matrices R created first using …
An Analysis Of Fourier Transform Infrared Spectroscopy Data To Predict Herpes Simplex Virus 1 Infection, Patrick D. Champion
An Analysis Of Fourier Transform Infrared Spectroscopy Data To Predict Herpes Simplex Virus 1 Infection, Patrick D. Champion
Mathematics Theses
The purpose of this analysis is to evaluate the usefulness of Fourier Transform Infrared (FTIR) spectroscopy in the detection of Herpes Simplex Virus 1 (hsv1) infection at an early stage. The raw absorption values were standardized to eliminate inter-sampling error. Wilcoxon-Mann-Whitney (WMW) statistic's Z score was calculated to select significant spectral regions. Partial least squares modeling was performed because of multicollinearity. Kolmogorov-Smirnov statistic showed models for healthy tissues from different time groups were not from same distribution. The additional 24 hour dataset was evaluated using the following methods. Variables were selected by WMW Z score. Difference of Composites statistic, DC, …
Semi-Parametric Inference For The Partial Area Under The Roc Curve, Fangfang Sun
Semi-Parametric Inference For The Partial Area Under The Roc Curve, Fangfang Sun
Mathematics Theses
Diagnostic tests are central in the field of modern medicine. One of the main factors for interpreting a diagnostic test is the discriminatory accuracy. For a continuous-scale diagnostic test, the area under the receiver operating characteristic (ROC) curve, AUC, is a useful one-number summary index for the diagnostic accuracy of the test. When only a particular region of the ROC curve would be of interest, the partial AUC (pAUC) is a more appropriate index for the diagnostic accuracy. In this thesis, we develop seven confidence intervals for the pAUC under the semi-parametric models for the diseased and non-diseased populations by …
Time Series Forecasting Model For Chinese Future Marketing Price Of Copper And Aluminum, Zhejin Hu
Time Series Forecasting Model For Chinese Future Marketing Price Of Copper And Aluminum, Zhejin Hu
Mathematics Theses
This thesis presents a comparison for modeling and forecasting Chinese futures market of copper and aluminum with single time series and multivariate time series under linear restrictions. For single time series, data transformation for stationary purpose has been tested and performed before ARIMA model was built. For multivariate time series, co-integration rank test has been performed and included before VECM model was built. Based on selected models, the forecasting shows multivariate time series analysis has a better result than single time series, which indicates utilizing the relationships among the series can improve the accuracy of time series forecasting.
Infrared Spectroscopy In Combination With Advanced Statistical Methods For Distinguishing Viral Infected Biological Cells, Tian Tang
Mathematics Theses
Fourier Transform Infrared (FTIR) microscopy is a sensitive method for detecting difference in the morphology of biological cells. In this study FTIR spectra were obtained for uninfected cells, and cells infected with two different viruses. The spectra obtained are difficult to discriminate visually. Here we apply advanced statistical methods to the analysis of the spectra, to test if such spectra are useful for diagnosing viral infections in cells. Logistic Regression (LR) and Partial Least Squares Regression (PLSR) were used to build models which allow us to diagnose if spectral differences are related to infection state of the cells. A three-fold, …
Some Conclusions Of Statistical Analysis Of The Spectropscopic Evaluation Of Cervical Cancer, Hailun Wang
Some Conclusions Of Statistical Analysis Of The Spectropscopic Evaluation Of Cervical Cancer, Hailun Wang
Mathematics Theses
To significantly improve the early detection of cervical precancers and cancers, LightTouch™ is under development by SpectRx Inc.. LightTouch™ identifies cancers and precancers quickly by using a spectrometer to analyze light reflected from the cervix. Data from the spectrometer is then used to create an image of the cervix that highlights the location and severity of disease. Our research is conducted to find the appropriate models that can be used to generate map-like image showing disease tissue from normal and further diagnose the cervical cancerous conditions. Through large work of explanatory variable search and reduction, logistic regression and Partial Least …
Hiv/Aids Relative Survival And Mean Residual Life Analysis, Xinjian Zhang
Hiv/Aids Relative Survival And Mean Residual Life Analysis, Xinjian Zhang
Mathematics Theses
HIV/Aids Relative Survival and Mean Residual Life Analysis BY XINJIAN ZHANG Under the Direction of Gengsheng (Jeff) Qin and Ruiguang (Rick) Song ABSTRACT Generalized linear models with Poisson error were applied to investigate HIV/AIDS relative survival. Relative excess risk for death within 3 years after HIV/AIDS diagnosis was significantly higher for non-Hispanic blacks, American Indians and Hispanics compared with Whites. Excess hazard for death was also higher in men injection drug users compared with men who have sex with men (MSM). The relative excess hazard of old HIV/AIDS patients is significantly higher compared with younger patients. When CD4 increased, the …
Noetherian Filtrations And Finite Intersection Algebras, Sara Malec
Noetherian Filtrations And Finite Intersection Algebras, Sara Malec
Mathematics Theses
This paper presents the theory of Noetherian filtrations, an important concept in commutative algebra. The paper describes many aspects of the theory of these objects, presenting basic results, examples and applications. In the study of Noetherian filtrations, a few other important concepts are introduced such as Rees algebras, essential powers filtrations, and filtrations on modules. Basic results on these are presented as well. This thesis discusses at length how Noetherian filtrations relate to important constructions in commutative algebra, such as graded rings and modules, dimension theory and associated primes. In addition, the paper presents an original proof of the finiteness …
New Non-Parametric Confidence Interval For The Youden, Haochuan Zhou
New Non-Parametric Confidence Interval For The Youden, Haochuan Zhou
Mathematics Theses
Youden index, a main summary index for the Receiver Operating Characteristic (ROC) curve, is a comprehensive measurement for the effectiveness of a diagnostic test. For a continuous-scale diagnostic test, the optimal cut-point for the positive of disease is the cut-point leading to the maximization of the sum of sensitivity and specificity. Finding the Youden index of the test is equivalent to maximize the sum of sensitivity and specificity for all the possible values of the cut-point. In this thesis, we propose a new non-parametric confidence interval for the Youden index. Extensive simulation studies are conducted to compare the relative performance …
Bootstrap And Empirical Likelihood-Based Semi-Parametric Inference For The Difference Between Two Partial Aucs, Xin Huang
Mathematics Theses
With new tests being developed and marketed, the comparison of the diagnostic accuracy of two continuous-scale diagnostic tests are of great importance. Comparing the partial areas under the receiver operating characteristic curves (pAUC) is an effective method to evaluate the accuracy of two diagnostic tests. In this thesis, we study the semi-parametric inference for the difference between two pAUCs. A normal approximation for the distribution of the difference between two pAUCs has been derived. The empirical likelihood ratio for the difference between two pAUCs is defined and its asymptotic distribution is shown to be a scaled chi-quare distribution. Bootstrap and …
Intersections Of Longest Paths And Cycles, Thomas Hippchen
Intersections Of Longest Paths And Cycles, Thomas Hippchen
Mathematics Theses
It is a well known fact in graph theory that in a connected graph any two longest paths must have a vertex in common. In this paper we will explore what happens when we look at k - connected graphs, leading us to make a conjecture about the intersection of any two longest paths. We then look at cycles and look at what would be needed to improve on a result by Chen, Faudree and Gould about the intersection of two longest cycles.
Singular Value Decomposition In Image Noise Filtering And Reconstruction, Tsegaselassie Workalemahu
Singular Value Decomposition In Image Noise Filtering And Reconstruction, Tsegaselassie Workalemahu
Mathematics Theses
The Singular Value Decomposition (SVD) has many applications in image processing. The SVD can be used to restore a corrupted image by separating significant information from the noise in the image data set. This thesis outlines broad applications that address current problems in digital image processing. In conjunction with SVD filtering, image compression using the SVD is discussed, including the process of reconstructing or estimating a rank reduced matrix representing the compressed image. Numerical plots and error measurement calculations are used to compare results of the two SVD image restoration techniques, as well as SVD image compression. The filtering methods …
"Clustering Categorical Response" Application To Lung Cancer Problems In Living Scales, Ling Guo
"Clustering Categorical Response" Application To Lung Cancer Problems In Living Scales, Ling Guo
Mathematics Theses
The study aims to estimate the ability of different grouping techniques on categorical response. We try to find out how well do they work? Do they really find clusters when clusters exist? We use Cancer Problems in Living Scales from the ACS as our categorical data variables and lung cancer survivors as our studying group. Five methods of cluster analysis are examined for their accuracy in clustering on both real CPILS dataset and simulated data. The methods include hierarchical cluster analysis (Ward's method), model-based clustering of raw data, model-based clustering of the factors scores from a maximum likelihood factor analysis, …
Riccati Equations In Optimal Control Theory, James Bellon
Riccati Equations In Optimal Control Theory, James Bellon
Mathematics Theses
It is often desired to have control over a process or a physical system, to cause it to behave optimally. Optimal control theory deals with analyzing and finding solutions for optimal control for a system that can be represented by a set of differential equations. This thesis examines such a system in the form of a set of matrix differential equations known as a continuous linear time-invariant system. Conditions on the system, such as linearity, allow one to find an explicit closed form finite solution that can be more efficiently computed compared to other known types of solutions. This is …
Direct Adjustment Method On Aalen's Additive Hazards Model For Competing Risks Data, Haci Mustafa Akcin
Direct Adjustment Method On Aalen's Additive Hazards Model For Competing Risks Data, Haci Mustafa Akcin
Mathematics Theses
Aalen’s additive hazards model has gained increasing attention in recently years because it model all covariate effects as time-varying. In this thesis, our goal is to explore the application of Aalen’s model in assessing treatment effect at a given time point with varying covariate effects. First, based on Aalen’s model, we utilize the direct adjustment method to obtain the adjusted survival of a treatment and comparing two direct adjusted survivals, with univariate survival data. Second, we focus on application of Aalen’s model in the setting of competing risks data, to assess treatment effect on a particular type of failure. The …
Algorithms For Toeplitz Matrices With Applications To Image Deblurring, Symon Kipyagwai Kimitei
Algorithms For Toeplitz Matrices With Applications To Image Deblurring, Symon Kipyagwai Kimitei
Mathematics Theses
In this thesis, we present the O(n(log n)^2) superfast linear least squares Schur algorithm (ssschur). The algorithm we will describe illustrates a fast way of solving linear equations or linear least squares problems with low displacement rank. This program is based on the O(n^2) Schur algorithm speeded up via FFT. The algorithm solves a ill-conditioned Toeplitz-like system using Tikhonov regularization. The regularized system is Toeplitz-like of displacement rank 4. We also show the effect of choice of the regularization parameter on the quality of the image reconstructed.
Sign Pattern Matrices That Require Almost Unique Rank, Assefa D. Merid
Sign Pattern Matrices That Require Almost Unique Rank, Assefa D. Merid
Mathematics Theses
A sign pattern matrix is a matrix whose entries are from the set {+,-, 0}. For a real matrix B, sgn(B) is the sign pattern matrix obtained by replacing each positive respectively, negative, zero) entry of B by + (respectively, -, 0). For a sign pattern matrixA, the sign pattern class of A, denoted Q(A), is defined as { B : sgn(B)= A }. The minimum rank mr(A)(maximum rank MR(A)) of a sign pattern matrix A is the minimum (maximum) of the ranks of the real matrices in Q(A). Several results concerning sign patterns A that require almost …
Treatments Of Chlamydia Trachomatis And Neisseria Gonorrhoeae, Ken Kun Zhao
Treatments Of Chlamydia Trachomatis And Neisseria Gonorrhoeae, Ken Kun Zhao
Mathematics Theses
Chlamydia Trachomatis and Neisseria Gonorrhoeae rank as the two most commonly reported sexually transmitted diseases (STDs) in the United States. Under limited budget, publicly funded clinics are not able to screen and treat the two diseases for all patients. They have to make a decision as to which group of population shall go through the procedure for screening and treating the two diseases. Therefore, we propose a cubic integer programming model on maximizing the number of units of cured diseases. At the same time, a two-step algorithm is established to solve the cubic integer program. We further develop a web-server, …
Generic Continuous Functions And Other Strange Functions In Classical Real Analysis, Douglas Albert Woolley
Generic Continuous Functions And Other Strange Functions In Classical Real Analysis, Douglas Albert Woolley
Mathematics Theses
In this paper we examine continuous functions which on the surface seem to defy well-known mathematical principles. Before describing these functions, we introduce the Baire Category theorem and the Cantor set, which are critical in describing some of the functions and counterexamples. We then describe generic continuous functions, which are nowhere differentiable and monotone on no interval, and we include an example of such a function. We then construct a more conceptually challenging function, one which is everywhere differentiable but monotone on no interval. We also examine the Cantor function, a nonconstant continuous function with a zero derivative almost everywhere. …
Becoming Critical Mathematics Pedagogues: A Journey, David W. Stinson, Carla R. Bidwell, Ginny C. Powell, Mary M. Thurman
Becoming Critical Mathematics Pedagogues: A Journey, David W. Stinson, Carla R. Bidwell, Ginny C. Powell, Mary M. Thurman
Middle-Secondary Education and Instructional Technology Faculty Publications
This session will report the findings of a study that explored the beginning transformations in the pedagogical philosophies and practices of three mathematics teachers (middle, high school, and 2-year college) who completed a graduate-level mathematics education course that focused on critical theory and teaching for social justice, and how these transformations are compatible (or not) with reform mathematics education as suggested by the National Council of Teachers of Mathematics (NCTM), and in turn, the new Georgia Performance Standards (GPS). The study employed Freirian participatory research methodology; in fact, the participants were not only coresearchers, but also co-authors of the study. …